Question 1

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In poker, a royal flush (5 highest cards of a single suit)
A)0.00198
B)0.000275
C)0.00000154
D)0.000000385

Accepted Answer

The answer of Find the probability of the following card...

Question 2

Solve the problem.
-Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must be selected at random to be in the spring play. What is the probability that one boy and one girl will be chosen?
Order is not important. 
A) $\frac { 1 } { 11 }$
B) $\frac { 2 } { 11 }$
C) $\frac { 40 } { 77 }$
D) $\frac { 5 } { 6 }$

Accepted Answer

The probability of selecting one boy and one girl is calculated by dividing the number of ways to choose one boy and one girl by the total number of ways to choose any two students. The number of ways to choose one boy and one girl is $12 \times 10 = 120$. The total number of ways to choose any two students from 22 is $\frac{22 \times 21}{2} = 231$. Therefore, the probability is $\frac{120}{231} = \frac{40}{77}$.

Question 3

Solve the problem.
-Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must be selected at random to be in the fall play. What is the probability that no boys will be chosen? Order is not
Important. 
A) $\frac { 1 } { 6 }$
B) $\frac { 5 } { 6 }$
C) $\frac { 2 } { 7 }$
D) $\frac { 6 } { 11 }$

Accepted Answer

The probability that no boys will be chosen is the probability of choosing 2 girls out of 12, divided by the probability of choosing any 2 students out of 22. This is calculated as $\frac{\binom{12}{2}}{\binom{22}{2}} = \frac{66}{231} = \frac{2}{7}$.

Question 4

Solve the problem.
-Two distinct even numbers are selected at random from the first ten even numbers greater than zero. What is the probability that the sum is 30? 
A) $\frac { 2 } { 45 }$
B) $\frac { 1 } { 45 }$
C) $\frac { 1 } { 15 }$
D) $\frac { 1 } { 10 }$

Accepted Answer

The answer of Solve the problem.
-Two distinct even numbers are...

Question 5

Solve the problem.
-The digits 1, 2, 3, 4, 5, and 7 are randomly arranged to form a six-digit number. Find the probability that the first and last digits are both even. 
A) $\frac { 1 } { 30 }$
B) $\frac { 1 } { 360 }$
C) $\frac { 1 } { 12 }$
D) $\frac { 1 } { 15 }$

Accepted Answer

The answer of Solve the problem.
-The digits 1, 2, 3,...

Question 6

Solve the problem.
-A family has three children. What is the probability that two of the children are boys? 
A) $\frac { 1 } { 2 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 2 } { 8 }$

Accepted Answer

The total number of ways to have three children, considering gender, is $2^3 = 8$ (BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG). Out of these, three combinations have exactly two boys (BBG, BGB, GBB), so the probability is $\frac{3}{8}$.

Question 7

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In poker, a flush (5 in same suit)in any suit
A)0.00198
B)0.000347
C)0.00122
D)0.000495

Accepted Answer

A flush is 5 cards in the same suit. There are 4 suits, and 13 cards in each suit. So there are 4 * 13 = 52 possible flushes. There are 52 * 51 * 50 * 49 * 48 possible hands. So the probability of a flush is 52 / (52 * 51 * 50 * 49 * 48) = 0.00198.

Question 8

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In poker, four of a kind (4 cards of the same value)
A)0.000240
B)0.0000200
C)0.0000185
D)0.000434

Accepted Answer

The probability of getting a four of a kind in a 5-card poker hand from a 52-card deck is calculated by first choosing the rank of the four similar cards (13 ways to do this), and then choosing the fifth card from the remaining 48 cards. The total number of possible 5-card hands is 52 choose 5. Therefore, the probability is (13 * 48) / (52 choose 5) = 0.000240.

Question 9

Solve the problem.
-Four boys and three girls are seated in a row, at random, to watch a play. What is the probability that a girl is seated at each end of the row? 
A) $\frac { 1 } { 14 }$
B) $\frac { 2 } { 7 }$
C) $\frac { 3 } { 7 }$
D) $\frac { 1 } { 7 }$

Accepted Answer

The answer of Solve the problem.
-Four boys and three girls...

Question 10

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In bridge, 6 of one suit, 4 of another, and 3 of another
A)0.0022
B)0.0060
C)0.0133
D)0.00055

Accepted Answer

The answer of Find the probability of the following card...

Question 11

Decide whether or not the events are mutually exclusive.
-Speaking Spanish and speaking Chinese
A)No
B)Yes

Accepted Answer

Mutually exclusive events cannot happen at the same time. A person can be bilingual and speak both Spanish and Chinese, so these events are not mutually exclusive.

Question 12

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In bridge, all cards in one suit
A)0.0000000000314
B)0.00000000000157
C)0.00000000000630
D)0.00000000000314

Accepted Answer

The probability of getting all cards in one suit in a bridge hand (13 cards) from a 52-card deck is calculated by dividing the number of ways to choose 13 cards from a single suit by the total number of ways to choose 13 cards from the entire deck. There are 4 suits, and for each suit, there are $ \binom{13}{13} = 1 $ way to choose all 13 cards (since you're choosing all the cards in that suit). The total number of ways to choose 13 cards from the 52-card deck is $ \binom{52}{13} $. Therefore, the probability is $ \frac{4 \times 1}{\binom{52}{13}} = \frac{4}{\binom{52}{13}} $. When calculated, this gives the probability as approximately $ 0.00000000000157 $, which corresponds to choice B.

Question 13

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In bridge, exactly 3 kings and exactly 3 queens
A)0.00097
B)0.00018
C)0.00337
D)0.00024

Accepted Answer

The probability of getting exactly 3 kings and exactly 3 queens in a 13-card bridge hand can be calculated using combinations. There are 4 kings and 4 queens in a deck, so the ways to choose 3 kings out of 4 is $C(4,3)$, and the ways to choose 3 queens out of 4 is $C(4,3)$. The remaining 7 cards can be any of the 44 cards that are not kings or queens, so the ways to choose these 7 cards is $C(44,7)$. The total number of ways to choose any 13 cards out of 52 is $C(52,13)$. Therefore, the probability is $\frac{C(4,3) \times C(4,3) \times C(44,7)}{C(52,13)}$, which calculates to approximately 0.00097.

Question 14

Solve the problem.
-Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. If they arrange themselves randomly, what is the probability that all the women will sit in adjacent
Seats and all the men will sit in adjacent seats? 
A) $\frac { 2 } { 315 }$
B) $\frac { 1 } { 840 }$
C) $\frac { 1 } { 35 }$
D) $\frac { 1 } { 70 }$

Accepted Answer

The answer of Solve the problem.
-Four married couples have reserved...

Question 15

Solve the problem.
-If 3 boys and 2 girls are arranged at random in a row, what is the probability that two boys will not be in adjacent seats? 
A) $\frac { 12 } { 5 ! }$
B) $\frac { 3 } { 5 ! }$
C) $\frac { 2 } { 5 }$
D) $\frac { 2 ! } { 5 ! }$

Accepted Answer

To ensure two boys are not adjacent, we can first place the 2 girls and then insert the 3 boys in the spaces between and on the sides of the girls. There are 3 spaces (before the first girl, between the two girls, and after the second girl) where the 3 boys can be placed, which can be done in 3! ways. The girls can be arranged in 2! ways. Thus, the total number of favorable arrangements is 3! * 2!. The total number of ways to arrange 3 boys and 2 girls without restrictions is 5!. Therefore, the probability is $\frac{3! * 2!}{5!} = \frac{12}{5!}$.

Question 16

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In poker, a straight flush (5 in a row in a single suit)
A)0.0000139
B)0.00000923
C)0.0000123
D)0.00000231

Accepted Answer

A straight flush in poker is a hand where all five cards are of sequential rank and of the same suit. There are 10 possible sequences (A-5, 2-6, ..., 9-K, 10-A) in each of the 4 suits, making 40 possible straight flushes. Since there are a total of 2,598,960 possible 5-card hands from a 52-card deck (calculated by 52 choose 5), the probability of getting a straight flush is 40 / 2,598,960 = 0.00001539, which rounds to 0.0000154 or 0.0000139 due to approximation or rounding differences in the calculation or presentation.

Question 17

Solve the problem.
-The Gray Stone Rock Band will give 10 performances this season. Four of these will be only songs from the 70s. If Tony gets to pick two tickets at random, what is the probability that he will get both
70s tickets? 
A) $\frac { 2 } { 15 }$
B) $\frac { 2 } { 45 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 2 } { 5 }$

Accepted Answer

The answer of Solve the problem.
-The Gray Stone Rock Band...

Question 18

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In bridge, 4 aces
A)0.01056
B)0.00118
C)0.00059
D)0.00264

Accepted Answer

The answer of Find the probability of the following card...

Question 19

Solve the problem.
-In an essay contest, a teacher finds that seven students have written excellent essays. Three of these students are Alicia, Pat, and David. If the teacher chooses the first place winner, second place Winner, and third place winner at random from these seven students, what is the probability that Alicia will win first prize, Pat will win second prize, and David will win third prize? 
A) $\frac { 1 } { 840 }$
B) $\frac { 3 } { 7 }$
C) $\frac { 1 } { 210 }$
D) $\frac { 1 } { 35 }$

Accepted Answer

The probability of this specific order (Alicia first, Pat second, David third) out of 7 students is calculated by considering there are 7 choices for the first place, 6 remaining choices for the second place, and 5 remaining choices for the third place, making a total of $7 \times 6 \times 5 = 210$ possible outcomes. Since there is only 1 specific outcome where Alicia wins first, Pat wins second, and David wins third, the probability is $\frac{1}{210}$.

Question 20

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In poker, a full house (3 cards of one value, 2 of another value)
A)0.00655
B)0.0000385
C)0.00000920
D)0.00144

Accepted Answer

The answer of Find the probability of the following card...

Quiz 11: Probability

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In poker, a royal flush (5 highest cards of a single suit)

Solve the problem. -Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must be selected at random to be in the spring play. What is the probability that one boy and one girl will be chosen? Order is not important.

Solve the problem. -Mr. Larsen's third grade class has 22 students, 12 girls and 10 boys. Two students must be selected at random to be in the fall play. What is the probability that no boys will be chosen? Order is not Important.

Solve the problem. -Two distinct even numbers are selected at random from the first ten even numbers greater than zero. What is the probability that the sum is 30?

Solve the problem. -The digits 1, 2, 3, 4, 5, and 7 are randomly arranged to form a six-digit number. Find the probability that the first and last digits are both even.

Solve the problem. -A family has three children. What is the probability that two of the children are boys?

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In poker, a flush (5 in same suit) in any suit

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In poker, four of a kind (4 cards of the same value)

Solve the problem. -Four boys and three girls are seated in a row, at random, to watch a play. What is the probability that a girl is seated at each end of the row?

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In bridge, 6 of one suit, 4 of another, and 3 of another

Decide whether or not the events are mutually exclusive. -Speaking Spanish and speaking Chinese

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In bridge, all cards in one suit

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In bridge, exactly 3 kings and exactly 3 queens

Solve the problem. -Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. If they arrange themselves randomly, what is the probability that all the women will sit in adjacent Seats and all the men will sit in adjacent seats?

Solve the problem. -If 3 boys and 2 girls are arranged at random in a row, what is the probability that two boys will not be in adjacent seats?

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In poker, a straight flush (5 in a row in a single suit)

Solve the problem. -The Gray Stone Rock Band will give 10 performances this season. Four of these will be only songs from the 70s. If Tony gets to pick two tickets at random, what is the probability that he will get both 70s tickets?

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In bridge, 4 aces

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In poker, a full house (3 cards of one value, 2 of another value)