Question 1

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-Suppose a hybrid mates with a pure dominant. If they produce two offspring, what is the probability that neither is a hybrid?
A)50
B) 125
C) 25
D) 75

Accepted Answer

When a hybrid (one dominant and one recessive gene) mates with a pure dominant (two dominant genes), the possible offspring genotypes are: 50% pure dominant and 50% hybrid. The probability that neither of the two offspring is a hybrid is the probability that both are pure dominant, which is 0.5 * 0.5 = 0.25 or 25%.

Question 2

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-Two hybrids produce a litter of four offspring. What is the probability that none of the four is pure recessive?
A) .316
B) .75
C). 0625
D) .004

Accepted Answer

When two hybrids (Aa) mate, the probability of producing a pure recessive (aa) is 1/4. The probability that none of the four offspring is pure recessive is (3/4)^4 = 0.316.

Question 3

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-Two hybrids produce a litter of four offspring. What is the probability that only the first one is pure recessive?
A).004
B) .105
C) .225
D) .422

Accepted Answer

The probability of a hybrid producing a pure recessive offspring is 1/4. The probability of the first being pure recessive and the others not is (1/4) * (3/4)^3 = 0.105.

Question 4

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-Two hybrids produce a litter of four offspring. What is the probability that exactly one is pure recessive?
A) .25
B) .422
C) .211
D).133

Accepted Answer

The answer of Solve the problem, rounding the answer as...

Question 5

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-In a population, $50 \%$ of females are pure dominant, $40 \%$ are hybrid, and $10 \%$ are pure recessive. If a pure recessive male mates with a random female and their first offspring has the dominant trait, what is the probability that the female is pure dominant?
A) .50
B) .75
C) .56
D) .34

Accepted Answer

The answer of Solve the problem, rounding the answer as...

Question 6

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-In a population, $40 \%$ of the females are pure dominant, $50 \%$ are hybrid, and $10 \%$ are pure recessive. If a pure recessive male mates with a random female and their first offspring has the dominant trait, what is the probability that the female is hybrid?
A) .50
B).56
C) .25
D) .17

Accepted Answer

The answer of Solve the problem, rounding the answer as...

Question 7

Solve the problem.
-If two fair dice are rolled, find the probability that the roll is a double given that the sum is 11 .
A) $\frac{1}{2}$
B) $\frac{1}{4}$
C) $\frac{1}{3}$
D) 0

Accepted Answer

A double means both dice show the same number. The only combinations that sum to 11 are (5,6) and (6,5), neither of which are doubles. Therefore, the probability is 0.

Question 8

Solve the problem.
-If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a spade, given that the first card was a spade.
A) $\frac{11}{51}$
B) $\frac{4}{17}$
C) $\frac{11}{12}$
D) $\frac{3}{13}$

Accepted Answer

The answer of Solve the problem.
-If two cards are drawn...

Question 9

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result.
-Th e second marble is red, given that the first marble is white.
A) $\frac{3}{28}$
B) $\frac{1}{4}$
C) $\frac{2}{7}$
D) $\frac{3}{32}$

Accepted Answer

There are 8 marbles in total. If the first marble is white, there are 7 marbles left, including 2 red ones. The probability of drawing a red marble second is $\frac{2}{7}$.

Question 10

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result.
-The second marble is blue, given that the first marble is white.
A) $\frac{3}{7}$
B) $\frac{1}{8}$
C) $\frac{3}{8}$
D) $\frac{1}{7}$

Accepted Answer

After drawing a white marble first, there are 7 marbles left (1 blue, 2 white, 2 green, 2 red). The probability of drawing a blue marble second is $\frac{1}{7}$.

Question 11

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result.
-The second marble is blue, given that the first marble is red.
A) $\frac{1}{8}$
B) $\frac{1}{7}$
C) $\frac{1}{4}$
D) $\frac{2}{7}$

Accepted Answer

If the first marble is red, there are 7 marbles left (1 blue, 3 white, 2 green, 1 red). The probability that the second marble is blue is $\frac{1}{7}$.

Question 12

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result.
-One marble is white, and one marble is blue.
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) $\frac{3}{56}$
D) $\frac{3}{28}$

Accepted Answer

The probability of drawing one white and one blue marble is calculated by finding the number of favorable outcomes divided by the total number of outcomes. There are 3 ways to choose a white marble and 1 way to choose a blue marble. The total number of ways to draw 2 marbles from 8 is $\binom{8}{2} = 28$. Thus, the probability is $\frac{3 \times 1}{28} = \frac{3}{28}$.

Question 13

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result.
-One marble is green, and one marble is red.
A) $\frac{1}{7}$
B) $\frac{3}{28}$
C) $\frac{1}{2}$
D) $\frac{1}{4}$

Accepted Answer

The answer of Assume that two marbles are drawn without...

Question 14

Decide whether the two events listed are independent.
-A fair die is rolled twice. $E$ is the event that the sum of the two rolls is eight and $T$ is the event that three appears on the first roll.

Accepted Answer

The events are not independent because the outcome of the first roll affects the possible outcomes for the sum to be eight. If a three appears on the first roll, the second roll must be a five for the sum to be eight, which is a specific condition influenced by the first roll.

Question 15

Decide whether the two events listed are independent.
-A fair die is rolled twice. F is the event that six appears on the first roll and $S$ is the event that six appears on the second roll.

Accepted Answer

The outcome of the first roll does not affect the outcome of the second roll, making the events independent.

Question 16

Decide whether the two events listed are independent.
-Two cards are selected, with replacement, from an ordinary deck. C is the event that a club appears on the first draw. A is the event that an ace appears on the second draw.

Accepted Answer

The events are independent because the outcome of the first draw does not affect the outcome of the second draw due to replacement.

Question 17

Decide whether the two events listed are independent.
-Two cards are selected, without replacement, from an ordinary deck. F is the event that an ace appears on the first draw. $S$ is the event that an ace appears on the second draw.

Accepted Answer

The events are not independent because the outcome of the first draw affects the probability of drawing an ace on the second draw.

Question 18

Find the probability.
-A calculator requires a keystroke assembly and a logic circuit. Assume that $80 \%$ of the keystroke assemblies and $81 \%$ of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.
A) .6561
B) .8100
C) .6480
D) .6400

Accepted Answer

The probability that both components are satisfactory is the product of their individual probabilities: $0.80 \times 0.81 = 0.648$.

Question 19

Find the probability.
-If two cards are drawn with replacement from an ordinary deck, find the probability the first card is a heart and the second is a diamond.
A) $\frac{1}{204}$
B) $\frac{1}{169}$
C) $\frac{13}{204}$
D) $\frac{1}{16}$

Accepted Answer

The probability of drawing a heart first is $ \frac{13}{52} = \frac{1}{4} $. Since the card is replaced, the probability of drawing a diamond second is also $ \frac{13}{52} = \frac{1}{4} $. Therefore, the combined probability is $ \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} $.

Question 20

Find the probability.
-In a certain city, $14 \%$ of the people are business executives, and $29 \%$ of the business executives drive Cadillacs. Assuming independent events, what is the probability of choosing a business executive who drives a Cadillac? Round the answer to the nearest hundredth.
A).04
B) .14
C) .29
D) .41

Accepted Answer

The probability of choosing a business executive is 0.14, and the probability that a business executive drives a Cadillac is 0.29. Assuming independence, multiply these probabilities: 0.14 * 0.29 = 0.0406, which rounds to 0.04.

Quiz 8: Sets and Probability

Solve the problem. -If two fair dice are rolled, find the probability that the roll is a double given that the sum is 11 .

Solve the problem. -If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a spade, given that the first card was a spade.

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -Th e second marble is red, given that the first marble is white.

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -The second marble is blue, given that the first marble is white.

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -The second marble is blue, given that the first marble is red.

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -One marble is white, and one marble is blue.

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -One marble is green, and one marble is red.

Decide whether the two events listed are independent. -A fair die is rolled twice. EEE is the event that the sum of the two rolls is eight and TTT is the event that three appears on the first roll.

Decide whether the two events listed are independent. -A fair die is rolled twice. F is the event that six appears on the first roll and SSS is the event that six appears on the second roll.

Decide whether the two events listed are independent. -Two cards are selected, with replacement, from an ordinary deck. C is the event that a club appears on the first draw. A is the event that an ace appears on the second draw.

Decide whether the two events listed are independent. -Two cards are selected, without replacement, from an ordinary deck. F is the event that an ace appears on the first draw. SSS is the event that an ace appears on the second draw.

Find the probability. -A calculator requires a keystroke assembly and a logic circuit. Assume that 80%80 \%80% of the keystroke assemblies and 81%81 \%81% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.

Find the probability. -If two cards are drawn with replacement from an ordinary deck, find the probability the first card is a heart and the second is a diamond.

Decide whether the two events listed are independent. -A fair die is rolled twice. $E$ is the event that the sum of the two rolls is eight and $T$ is the event that three appears on the first roll.

Decide whether the two events listed are independent. -A fair die is rolled twice. F is the event that six appears on the first roll and $S$ is the event that six appears on the second roll.

Decide whether the two events listed are independent. -Two cards are selected, without replacement, from an ordinary deck. F is the event that an ace appears on the first draw. $S$ is the event that an ace appears on the second draw.

Find the probability. -A calculator requires a keystroke assembly and a logic circuit. Assume that $80 \%$ of the keystroke assemblies and $81 \%$ of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.