Question 1

There are 10 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are possible?
A) 10,000
B) 210
C) 24
D) 5040

Accepted Answer

The number of ways to choose 4 members from 10 is calculated using combinations: C(10, 4) = 10! / (4!(10-4)!) = 210.

Question 2

Find the indicated complement.
-If $P ( A ) = \frac { 2 } { 19 }$, find $P ( \bar { A } )$
A) 0

B) $\frac { 19 } { 2 }$

C) $\frac { 2 } { 21 }$

D) $\frac { 17 } { 19 }$

Accepted Answer

The complement of an event A, denoted as $ \bar{A} $, is calculated as $ P(\bar{A}) = 1 - P(A) $. Given $ P(A) = \frac{2}{19} $, the complement is $ P(\bar{A}) = 1 - \frac{2}{19} = \frac{17}{19} $.

Question 3

From the information provided, create the sample space of possible outcomes.
-Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible
Outcomes.
A) WW, WW 
B) WW, BW 
C) WB, BW 
D) WW, BB

Accepted Answer

The male mouse can pass either a white (W) or black (B) gene, while the female can only pass a white (W) gene. Thus, the possible combinations for the offspring are WW (white from both parents) and BW (white from the female and black from the male).

Question 4

The table below describes the smoking habits of a group of asthma sufferers.

$\begin{array}{r|ccccr} 
&&\text { Occasional }&\text {Regular}&\text { Heavy }\
& \text { Nonsmoker } & \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \
\hline \text { Men } & 367 & 50 & 65 & 47 & 529 \
\text { Women } & 316 & 31 & 70 & 45 & 462 \
\text { Total } & 683 & 81 & 135 & 92 & 991
\end{array}$
 If one of the 991 people is randomly selected, find the probability of getting a regular or heavy smoker.
A) 0.229
B) 0.493
C) 0.136
D) 0.113

Accepted Answer

The answer of The table below describes the smoking habits...

Question 5

Evaluate the expression
-${ } _ { 10 } \mathrm { P } _ { 3 }$

A) 27
B) 720
C) 7
D) 120

Accepted Answer

The answer of Evaluate the expression
-\({ } _ { 10...

Question 6

In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?
A) 1 : 3
B) 1 : 4
C) 3 : 4
D) 3 : 1

Accepted Answer

The probability of selecting someone who commutes by bicycle is 25%, or 1/4. The odds against this are the ratio of those who do not commute by bicycle (3/4) to those who do (1/4), which simplifies to 3:1.

Question 7

Find the indicated probability.
-You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction.

A) $\frac { 2 } { 13 }$

B) $\frac { 13 } { 102 }$

C) $\frac { 4 } { 663 }$

D) $\frac { 1 } { 663 }$

Accepted Answer

The probability of drawing a King first is $ \frac{4}{52} $. After drawing a King, there are 51 cards left, and the probability of drawing a Queen is $ \frac{4}{51} $. Thus, the probability is $ \frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = \frac{4}{663} $.

Question 8

Is Event B dependent or independent of Event A?
-A: A green ball is drawn from a box with five balls and placed next to the box. B: A red ball is drawn next and placed next to the green one.

A) Dependent
B) Independent

Accepted Answer

Event B is dependent on Event A because the outcome of Event A (a green ball being drawn and placed next to the box) affects the probability of Event B occurring (a red ball being drawn and placed next to the green one). Specifically, if a green ball had not been drawn in Event A, then there would be no green ball to place next to the box and therefore no opportunity for a red ball to be drawn and placed next to it in Event B.

Question 9

From the information provided, create the sample space of possible outcomes.
-Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%. 
A) N NN NR NNN NRN
B) NR NNR NNR
C) NNR NNN
D) NNN RNN NR

Accepted Answer

The sample space for the fifth litter, given the previous outcomes and assuming a 50% probability for each, is either three normal pups (NNN) or two normal pups and a runt (NNR).

Question 10

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
-The table below shows the soft drinks preferences of people in three age groups. $$\begin{array} { r | c c c } 
& \text { cola } & \text { root beer } & \text { lemon-lime } \
\hline \text { under 21 years of age } & 40 & 25 & 20 \
\text { between 21 and 40 } & 35 & 20 & 30 \
\text { over 40 years of age } & 20 & 30 & 35
\end{array}$$ 
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and drinks cola. 
A) $\frac { 4 } { 51 }$

B) $\frac { 4 } { 17 }$

C) $\frac { 4 } { 19 }$

D) None of the above is correct.

Accepted Answer

The probability that the person is over 40 is $\frac { 85 } { 255 }$. The probability that the person drinks cola is $\frac { 20 } { 85 }$. The probability that the person is over 40 and drinks cola is $\frac { 20 } { 255 } = \frac { 4 } { 51 }$.

Question 11

Is Event B dependent or independent of Event A?
-A: A mosquito lands on your arm. 
B: You get a mosquito bite.

A) Independent
B) Dependent

Accepted Answer

Event B is dependent on Event A because getting a mosquito bite is contingent upon a mosquito landing on your arm.

Question 12

Find the indicated probability.
-When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 3 times, what is the probability of getting a sum of 5 every time? Round to eight decimal places.

A) 0.00267918
B) 0.00137174
C) 0.0667
D) 0.008

Accepted Answer

The probability of getting a sum of 5 with one roll of two dice is 4/36 or 1/9. Rolling the dice three times independently, the probability of getting a sum of 5 each time is (1/9)^3 = 0.00137174.

Question 13

Use Bayes' theorem to find the indicated probability.
-Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector test, 63% of lies are identified as lies and that 16% of true statements are also identified as lies.
A company gives its job applicants a polygraph test, asking "Did you tell the truth on your job application?". Suppose that 90% of the job applicants tell the truth during the polygraph test.
What is the probability that a person who fails the test was actually telling the truth?
A) 0.438
B) 0.696
C) 0.304
D) 0.16

Accepted Answer

The answer of Use Bayes' theorem to find the indicated...

Question 14

Find the indicated probability. Round to the nearest thousandth.
-A sample of 4 different calculators is randomly selected from a group containing 14 that are defective and 39 that have no defects. What is the probability that at least one of the calculators is
Defective?
A) 0.281
B) 0.719
C) 0.707
D) 0.140

Accepted Answer

The probability that at least one calculator is defective is 1 minus the probability that none are defective. The probability that none are defective is calculated by choosing 4 non-defective calculators from the 39 available, divided by choosing any 4 calculators from the total 53. This gives: 1 - [(39/53) * (38/52) * (37/51) * (36/50)] = 0.719.

Question 15

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-If you are told that a mystery person's name begins with a consonant, would it be "unusual" to guess the first letter of that person's name?
A) Yes
B) No

Accepted Answer

The answer of Answer the question, considering an event to...

Question 16

Express the indicated degree of likelihood as a probability value.
-"It will definitely turn dark tonight."
A) 1
B) 0.5
C) 0.67
D) 0.30

Accepted Answer

The word "definitely" implies 100% certainty, so the probability of it turning dark tonight is 1.

Question 17

The table below describes the smoking habits of a group of asthma sufferers. 
$\begin{array}{r|cccr} 
& &\text { Light } & \text { Heavy }\
& \text { Nonsmoker } & \text { smoker } & \text { smoker } & \text { Total } \
\hline \text { Men } & 404 & 34 & 32 & 470 \
\text { Women } & 375 & 39 & 50 & 464 \
\text { Total } & 779 & 73 & 82 & 934
\end{array}$

If two different people are randomly selected from the 934 subjects, find the probability that they are both women. Round to four decimal places.
A) 0.2465
B) 0.000004645
C) 0.2468
D) 0.1612

Accepted Answer

The probability of selecting a woman is 464/934. The probability of selecting two women is (464/934) * (464/934) = 0.2465 (rounded to four decimal places).

Question 18

Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
A) 0.3333
B) 0.00000002
C) 0.0082
D) 0.00000751

Accepted Answer

The probability that the second person has the same birthday as the first is 1/365, and the probability that the third person also has the same birthday is 1/365. Therefore, the probability that all three have the same birthday is (1/365) * (1/365) = 1/133225, which is approximately 0.00000751.

Question 19

Find the indicated probability.
-A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.
A) 0.0144
B) 0.176
C) 0.7744
D) 0.7733

Accepted Answer

The probability of selecting a good coil on the first draw is 88/100. Since the first coil is replaced, the probability of selecting a good coil on the second draw is also 88/100. Therefore, the probability of both events occurring is (88/100) * (88/100) = 0.7744.

Question 20

A 6-sided die is rolled. Find P(3 or 5).

A) $\frac { 1 } { 6 }$

B) $\frac { 1 } { 3 }$

C) 2

D) $\frac { 1 } { 36 }$

Accepted Answer

The probability of rolling a 3 or a 5 on a 6-sided die is the sum of the probabilities of each event. Each number has a probability of $\frac{1}{6}$, so P(3 or 5) = $\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$.

Quiz 4: Probability

There are 10 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are possible?

Find the indicated complement. -If $P ( A ) = \frac { 2 } { 19 }$ , find $P ( \bar { A } )$

Evaluate the expression - ${ } _ { 10 } \mathrm { P } _ { 3 }$

In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?

Find the indicated probability. -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction.

Is Event B dependent or independent of Event A? -A: A green ball is drawn from a box with five balls and placed next to the box. B: A red ball is drawn next and placed next to the green one.

From the information provided, create the sample space of possible outcomes. -Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%.

Is Event B dependent or independent of Event A? -A: A mosquito lands on your arm. B: You get a mosquito bite.

Find the indicated probability. -When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 3 times, what is the probability of getting a sum of 5 every time? Round to eight decimal places.

Find the indicated probability. Round to the nearest thousandth. -A sample of 4 different calculators is randomly selected from a group containing 14 that are defective and 39 that have no defects. What is the probability that at least one of the calculators is Defective?

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -If you are told that a mystery person's name begins with a consonant, would it be "unusual" to guess the first letter of that person's name?

Express the indicated degree of likelihood as a probability value. -"It will definitely turn dark tonight."

Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

Find the indicated probability. -A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.

A 6-sided die is rolled. Find P(3 or 5) .