Event 2A
Given the following event:
Given an urn containing 2 black, 3 yellow, and 5 orange balls. Two balls are drawn and the first ball is not replaced before the second is drawn.
-Given Event 2A, what is the probability that the two balls are the same color?
A) 7/25
B) 19/45
C) 14/45
D) 8/25
E) 1/4

Question

Quizplus · Accepted Answer

There are three cases where two balls of the same color can be drawn:
1) Two black balls
2) Two yellow balls
3) Two orange balls
Using the formula for conditional probability, P(A | B) = P(A ∩ B) / P(B), we can find the probability of each case:
1) P(2 black balls) = (2/10) * (1/9) = 1/45
2) P(2 yellow balls) = (3/10) * (2/9) = 1/15
3) P(2 orange balls) = (5/10) * (4/9) = 20/90 = 2/9
The total probability of these three cases is (1/45) + (1/15) + (2/9) = 0.3111, or approximately 14/45, which is answer choice C.

Event 2A Given the Following Event