Conditional Probability and Multiplication Rule

A box contains 6 white balls and 4 black balls. What is the probability of drawing a white ball followed by a black ball without replacement?

• 2/5

• 4/15

• 5/15

• 3/10

Answer explanation

The probability of drawing a white ball first is 6/10. After removing one white ball, the probability of drawing a black ball is 4/9. Multiplying these probabilities gives 4/15.

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.

A box contains 3 yellow balls, 2 green balls, and 1 red ball. Two balls are taken without replacement. What is the probability of drawing a yellow ball given that the first ball is a green ball?

• 1/5

• 1/6

• 2/5

• 1/3

Answer explanation

P(Yellow|Green)=P(Green n Yellow)/P(Green)

P(Green n Yellow)=2/6*3/5=1/5

P(Green)=2/6=1/3

Then P(Yellow|Green)=(1/5)/(1/3)=3/5

What is the probability that they speak French given they are a girl? 

• 2.14

• .24

• .4

• .8571

What is the probability that a female is chose given they like a Toyota? 

• .525

• .4627

• .6774

• .3143

What is P(not sport | Foreign language)?

• 23/37

• 14/23

• 14/37

• 3/23

What is the probability that the person picked will be a boy given they speak german? 

• .7273

• .4

• .16

• .22

What is the probability that a student plays on a sports team given they play an instrument?

• .7273

• .8

• .55

• .2222

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 a Visa and AA card, given they hold a Visa.

• .0267

• .02

• .3333

• 37.5

What is P(Foreign language | Sport)?

• 14/27

• 7/12

• 23/47

• 37/47