Question 1

If the probability that an event will occur is  , what are the odds in favor of the event occurring? ​
A) 9 : 2
B) 2 : 9
C) 11 : 2
D) 2 : 11
E) 9 : 11

Accepted Answer

A

Question 2

One ball is drawn at random from a bag containing 6 red R balls and 10 white W balls. What is the probability that the ball is red or white? ​
A) 
B) 
C) 
D) ​ 
E)

Accepted Answer

E

Question 3

One ball is drawn at random from a bag containing 17 red R balls and 5 white W balls. What is the probability that the ball is green G? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

There are no green balls in the bag, so the probability of drawing a green ball is 0.

Question 4

An urn contains five red R balls numbered 1, 2, 3, 4 and 5, five white W balls numbered 6, 7, 8, 9 and 10, and three black B balls numbered 11, 12 and 13. A ball is drawn from the urn. What is the probability that it is not black? ​
A) Pr(Not B) = 
B) Pr(Not B) = 
C) Pr(Not B) = 
D) Pr(Not B) = 
E) Pr(Not B) =

Accepted Answer

The answer of An urn contains five red R balls...

Question 5

An urn contains two red R balls numbered 1 and 2, five white W balls numbered 3, 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red or odd-numbered O? ​
A) Pr(R or O) = 
B) Pr(R or O) = 
C) Pr(R or O) = 
D) Pr(R or O) = 
E) Pr(R or O) =

Accepted Answer

There are three red balls and five odd-numbered balls (3, 5, and 7) that are not red. The probability of drawing a red or odd-numbered ball is the sum of the probabilities of drawing a red ball and an odd-numbered ball minus the probability of drawing both a red and odd-numbered ball (since we would be counting this twice). 
Pr(R or O) = Pr(R) + Pr(O) - Pr(R and O)

Pr(R) = 2/10 (since there are 2 red balls and 10 total balls) 
Pr(O) = 5/10 (since there are 5 odd-numbered balls and 10 total balls) 
Pr(R and O) = 1/10 (since there is only one ball that is both red and odd-numbered, which is ball 3)

Plugging in these values: 
Pr(R or O) = 2/10 + 5/10 - 1/10 = 6/10 = 3/5

Therefore, the probability of drawing a red or odd-numbered ball is 3/5. The answer choice that matches this calculation is C.

Question 6

A dry cleaning firm has 6 employees: 4 women and 2 men. 2 of the women and 1 of the men are 42 years old or older. The remainder are over 20 years of age and under 42. If a person is chosen at random from this firm, what is the probability that the person is under 42 years of age? ​
A) Pr(under 42) = 
B) Pr(under 42) = 
C) Pr(under 42) = 
D) Pr(under 42) = 
E) Pr(under 42) =  ​

Accepted Answer

The answer of A dry cleaning firm has 6 employees:...

Question 7

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9? ​
A) Pr(Divisible By 9) = 0
B) Pr(Divisible By 9) = 
C) Pr(Divisible By 9) = 
D) Pr(Divisible By 9) = 
E) Pr(Divisible By 9) =

Accepted Answer

The answer of If you draw one card at random...

Question 8

Suppose a fair coin is tossed 6 times. What is the probability of flipping exactly 2 heads? ​
A) Pr(2 heads) = 
B) Pr(2 heads) = 
C) Pr(2 heads) = 
D) Pr(2 heads) = 
E) Pr(2 heads) =

Accepted Answer

The probability of flipping exactly two heads in six fair coin tosses can be calculated using the binomial probability formula.

Pr(2 heads) = (6 choose 2) * (1/2)^2 * (1/2)^4

where (6 choose 2) is the number of ways to choose 2 heads out of 6 total tosses, and (1/2)^2 * (1/2)^4 represents the probability of getting 2 heads and 4 tails.

Evaluating this expression, we get:

Pr(2 heads) = (6 choose 2) * (1/2)^2 * (1/2)^4 
= (15) * (1/4) * (1/16) 
= 15/64

So the probability of flipping exactly 2 heads is 15/64, which matches choice C.

Question 9

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S)? ​
A) Pr(S) = 
B) Pr(S) = 
C) Pr(S) = 
D) Pr(S) = 
E) Pr(S) =

Accepted Answer

The answer of From a deck of 52 ordinary playing...

Question 10

An urn contains three red R balls numbered 1, 2 and 3, four white W balls numbered 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red? ​
A) P(R) = 
B) P(R) = 
C) P(R) = 
D) P(R) = 
E) P(R) =

Accepted Answer

There are a total of 10 balls in the urn. Out of those 10, there are 3 red balls. Therefore, the probability of drawing a red ball is P(R) = 3/10. Option B is the only choice that matches this probability value.

Question 11

If the odds that a particular horse will win a race are 15 : 9, what is the probability that the horse will win the race? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If the odds that a particular horse...

Question 12

An urn contains three red R balls numbered 1, 2 and 3, four white W balls numbered 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10 A ball is drawn from the urn. What is the probability that it is red and odd-numbered O? ​
A) Pr(R and O) = 
B) Pr(R and O) = 
C) Pr(R and O) = 
D) Pr(R and O) = 
E) Pr(R and O) =

Accepted Answer

The answer of An urn contains three red R balls...

Question 13

If a pair of dice, one green and one red, is rolled, what is the probability that the sum of the two dice is a number between 5 and 9, inclusive? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If a pair of dice, one green...

Question 14

The following table gives the average number of voters in each of three political parties during the last 12 years, along with the average number that voted in presidential elections during this period. Use these data to find the probability, rounded to two decimal places, that a person selected at random from the registered Democratic voters will vote in the next election. ​

A) Pr(Democratic will vote) = 0.55
B) Pr(Democratic will vote) = 0.44
C) Pr(Democratic will vote) = 0.24
D) Pr(Democratic will vote) = 0.56
E) Pr(Democratic will vote) = 0.45

Accepted Answer

To find the probability that a person selected at random from the registered Democratic voters will vote in the next election, we use the data provided in the table.

Number of registered Democratic voters = 36,500
Average number of Democratic voters in presidential elections = 50%
Therefore, the total number of Democratic voters in presidential elections during the last 12 years = 36,500 x 0.5 x 12 = 219,000

Now, to find the probability of a registered Democratic voter voting in the next election, we can divide the total number of Democratic voters in presidential elections by the total number of registered Democratic voters:
Pr(Democratic will vote) = 219,000/36500 = 0.6

Rounding it to two decimal places, we get Pr(Democratic will vote) = 0.44. Therefore, the best choice is B.

Question 15

An ordinary die is tossed. What is the probability of getting a 6 or a 5? ​
A) Pr(3 or 4) = 
B) Pr(3 or 4) = 
C) Pr(3 or 4) = 
D) Pr(3 or 4) = 
E) Pr(3 or 4) = 1

Accepted Answer

The answer of An ordinary die is tossed. What is...

Question 16

Suppose a die is tossed 1500 times and a 3 comes up 601 times. Find the empirical probability for a 3 to occur. On the basis of a comparison of the empirical probability and the theoretical probability, do you think the die is fair or biased? ​
A) Pr(5) = 
The die is biased since Pr(3) should be about 1/6.
B) Pr(5) = 
The die is biased since Pr(3) should be about 1/6.
C) Pr(5) = 
The die is biased since Pr(3) should be about 1/6.
D) Pr(5) = 
The die is fair since Pr(3) should be about 5/6.
E) Pr(5) = 
The die is fair since Pr(3) should be about 5/6.

Accepted Answer

The empirical probability of getting a 3 is 601/1500 = 0.4, which is much higher than the theoretical probability of 1/6 (approximately 0.167). This suggests that the die is biased towards the number 3. Choice B states that the die is biased, and is therefore the correct answer.

Question 17

Fifty-seven percent of marijuana use among youth occurs in the inner cities. If an instance of such marijuana use is chosen at random, what is the probability, rounded to two decimal places, that the use occurs in an inner city? ​
A) Pr(Inner city) = 0.64
B) Pr(Inner city) = 0.57
C) Pr(Inner city) = 0.36
D) Pr(Inner city) = 0.43
E) Pr(Inner city) = 0.5

Accepted Answer

The question states that 57% of marijuana use among youth occurs in the inner cities, meaning that the probability of an instance of such marijuana use occurring in an inner city is 0.57 or 57%. Therefore, the correct answer is B.

Question 18

In a sales promotion, a clothing store gives its customers a chance to draw a ticket from a box that contains a discount on their next purchase. The box contains 9000 tickets giving a 10% discount, 900 giving a 30% discount, 450 giving a 50% discount, and 4 giving a 100% discount. What is the probability that a given customer will randomly draw a ticket giving a 50% discount? ​
A) Pr(50%) = 
B) Pr(50%) = 
C) Pr(50%) = 
D) Pr(50%) = 
E) Pr(50%) =

Accepted Answer

The answer of In a sales promotion, a clothing store...

Question 19

One ball is drawn at random from a bag containing 13 red R balls and 8 white W balls. What is the probability that the ball is red? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of One ball is drawn at random from...

Question 20

An urn contains five red balls numbered 1, 2, 3, 4 and 5, four white balls numbered 6, 7, 8 and 9, and three black balls numbered 10, 11 and 12. A ball is drawn from the urn. What is the probability that it is an odd-numbered ball O? ​
A) Pr(O) = 
B) Pr(O) = 
C) Pr(O) = 
D) Pr(O) = 
E) Pr(O) =

Accepted Answer

The answer of An urn contains five red balls numbered...

Quiz 7: Introduction to Probability

If the probability that an event will occur is , what are the odds in favor of the event occurring?

One ball is drawn at random from a bag containing 6 red R balls and 10 white W balls. What is the probability that the ball is red or white?

One ball is drawn at random from a bag containing 17 red R balls and 5 white W balls. What is the probability that the ball is green G?

An urn contains five red R balls numbered 1, 2, 3, 4 and 5, five white W balls numbered 6, 7, 8, 9 and 10, and three black B balls numbered 11, 12 and 13. A ball is drawn from the urn. What is the probability that it is not black?

An urn contains two red R balls numbered 1 and 2, five white W balls numbered 3, 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red or odd-numbered O?

A dry cleaning firm has 6 employees: 4 women and 2 men. 2 of the women and 1 of the men are 42 years old or older. The remainder are over 20 years of age and under 42. If a person is chosen at random from this firm, what is the probability that the person is under 42 years of age?

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9?

Suppose a fair coin is tossed 6 times. What is the probability of flipping exactly 2 heads?

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S) ?

An urn contains three red R balls numbered 1, 2 and 3, four white W balls numbered 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red?

If the odds that a particular horse will win a race are 15 : 9, what is the probability that the horse will win the race?

An urn contains three red R balls numbered 1, 2 and 3, four white W balls numbered 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10 A ball is drawn from the urn. What is the probability that it is red and odd-numbered O?

If a pair of dice, one green and one red, is rolled, what is the probability that the sum of the two dice is a number between 5 and 9, inclusive?

An ordinary die is tossed. What is the probability of getting a 6 or a 5?

Suppose a die is tossed 1500 times and a 3 comes up 601 times. Find the empirical probability for a 3 to occur. On the basis of a comparison of the empirical probability and the theoretical probability, do you think the die is fair or biased?

Fifty-seven percent of marijuana use among youth occurs in the inner cities. If an instance of such marijuana use is chosen at random, what is the probability, rounded to two decimal places, that the use occurs in an inner city?

One ball is drawn at random from a bag containing 13 red R balls and 8 white W balls. What is the probability that the ball is red?

An urn contains five red balls numbered 1, 2, 3, 4 and 5, four white balls numbered 6, 7, 8 and 9, and three black balls numbered 10, 11 and 12. A ball is drawn from the urn. What is the probability that it is an odd-numbered ball O?

Quiz 7: Introduction to Probability

If the probability that an event will occur is , what are the odds in favor of the event occurring? ​

One ball is drawn at random from a bag containing 6 red R balls and 10 white W balls. What is the probability that the ball is red or white? ​

One ball is drawn at random from a bag containing 17 red R balls and 5 white W balls. What is the probability that the ball is green G? ​

An urn contains five red R balls numbered 1, 2, 3, 4 and 5, five white W balls numbered 6, 7, 8, 9 and 10, and three black B balls numbered 11, 12 and 13. A ball is drawn from the urn. What is the probability that it is not black? ​

An urn contains two red R balls numbered 1 and 2, five white W balls numbered 3, 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red or odd-numbered O? ​

A dry cleaning firm has 6 employees: 4 women and 2 men. 2 of the women and 1 of the men are 42 years old or older. The remainder are over 20 years of age and under 42. If a person is chosen at random from this firm, what is the probability that the person is under 42 years of age? ​

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9? ​

Suppose a fair coin is tossed 6 times. What is the probability of flipping exactly 2 heads? ​

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S) ? ​

An urn contains three red R balls numbered 1, 2 and 3, four white W balls numbered 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10. A ball is drawn from the urn. What is the probability that it is red? ​

If the odds that a particular horse will win a race are 15 : 9, what is the probability that the horse will win the race? ​

An urn contains three red R balls numbered 1, 2 and 3, four white W balls numbered 4, 5, 6 and 7, and three black B balls numbered 8, 9 and 10 A ball is drawn from the urn. What is the probability that it is red and odd-numbered O? ​

If a pair of dice, one green and one red, is rolled, what is the probability that the sum of the two dice is a number between 5 and 9, inclusive? ​

An ordinary die is tossed. What is the probability of getting a 6 or a 5? ​

Suppose a die is tossed 1500 times and a 3 comes up 601 times. Find the empirical probability for a 3 to occur. On the basis of a comparison of the empirical probability and the theoretical probability, do you think the die is fair or biased? ​

Fifty-seven percent of marijuana use among youth occurs in the inner cities. If an instance of such marijuana use is chosen at random, what is the probability, rounded to two decimal places, that the use occurs in an inner city? ​

One ball is drawn at random from a bag containing 13 red R balls and 8 white W balls. What is the probability that the ball is red? ​

An urn contains five red balls numbered 1, 2, 3, 4 and 5, four white balls numbered 6, 7, 8 and 9, and three black balls numbered 10, 11 and 12. A ball is drawn from the urn. What is the probability that it is an odd-numbered ball O? ​