Conditional Probability and Independence

Given the following VENN Diagram answer the following.
P( A | B )

• 2

• .4

• .6

• .8

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

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 the following VENN Diagram answer the following

P( B | A )

• .4

• .25

• .5

• .67

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

What is P(T given C)?

• 45%

• 29.6%

• 40%

• 33.3%

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

• 2.6

• .12

• .24

• .38