Use the Rule of Total Probability
-Suppose that there are two buckets. Bucket 1 contains 3 tennis balls and 5 ping -pong balls. Bucket 2 contains 4 tennis balls, 3 ping-pong balls, and 5 baseballs. An unfair coin will decide from which bucket we draw. Heads implies we draw from Bucket 1 and tails implies we draw from Bucket 2 . The probability of a heads is $\frac { 1 } { 3 }$ and the probability of a tails is $\frac { 2 } { 3 }$. What is the probability of drawing a baseball?
A) $0.277$
B) $0.723$
C) $0.25$
D) $0.417$

Question

Quizplus · Accepted Answer

The probability of drawing a baseball is the sum of the probabilities of drawing a baseball from Bucket 1 and Bucket 2, weighted by the probabilities of drawing from each bucket. The probability of drawing a baseball from Bucket 1 is 0, since there are no baseballs in Bucket 1. The probability of drawing a baseball from Bucket 2 is 5/12, since there are 5 baseballs in Bucket 2 and 12 total balls in Bucket 2. The probability of drawing from Bucket 1 is 1/3, and the probability of drawing from Bucket 2 is 2/3. Therefore, the probability of drawing a baseball is (0 * 1/3) + (5/12 * 2/3) = 5/18 = 0.277.

Use the Rule of Total Probability -Suppose That There Are 13\frac { 1 } { 3 }31​

Use the Rule of Total Probability
-Suppose That There Are $\frac { 1 } { 3 }$