Conditional Probability and Multiplication Rule

A new credit card has been issued to 2000 customers. Of these customers, 1500 hold a Visa, 500 hold an AA card, and 40 hold a Visa and AA card. Find the probability that a random chosen customer holds an AA, given they hold a Visa.

• .0267

• 37.5

• .02

• .3333

P(Sandals|Pants):

• 4/20

• 6/15

• 1/2

• 2/7

A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.34, and the probability of selecting a black marble on the first draw is 0.47. What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black?

• 16%

• 1.38%

• 72.3%

• Not enough information

45% total of the children in a school have a dog, 30% total have a cat, and 18% have a dog and cat. What percent of those who have a cat also have a dog?

• 60%

• 40%

• 24%

• 1.7%

P(Pizza|Senior):

• 10/15

• 4/5

• 2/3

• 10/5

Given P(A) = .8 and P( B| A) = .3, find P( A and B).

• 2.6

• .12

• .24

• .38

The weather forecaster predicted it will be 4/5 chance of rain for Monday and 2/3 chance of rain for Tuesday. What is the probability it will rain both days?

• 1/2

• 20/15

• 8/15

• 6/8

If the probability of event A is 0.3 and the probability of event B given A has occurred is 0.6, what is the conditional probability of event A given B?

• 0.5

• 0.4

• 0.3

• 0.7

Answer explanation

The conditional probability of event A given B is calculated using Bayes' theorem:

P(A|B) =[ P(B|A) * P(A)] / P(B)

Substituting the given values, we get P(A|B) =( 0.6 * 0.3) / P(B)

Since P(B) = P(B|A) * P(A) + P(B|A') * P(A') =(0.6 * 0.3) + (0.6 * 0.7) = 0.6,

then P(A|B)=(0.6 * 0.3) / 0.6 = 0.3.

If the probability of event A is 0.4 and the probability of event B is 0.3, what is the probability of both events occurring if both events are independent?

• 0.12

• 0.5

• 0.25

• 0.07

Answer explanation

The probability of both independent events occurring is the product of their individual probabilities, so 0.4 * 0.3 = 0.12.

If P(A)=0.6 and the P(B|A)=0.8, what is P(A∩B)?

• 0.2

• 0.25

• 0.75

• 0.48

Answer explanation

To find P(A∩B), use the formula P(A∩B) = P(A) * P(B|A) = 0.6 * 0.8 = 0.48. Therefore, the correct answer is 0.48.