BTGModeratorVI wrote: ↑Thu Aug 20, 2020 7:09 am
A box contains 1 blue ball, 1 yellow ball, and 2 red balls. Three balls are randomly selected (one after the other) without replacement. What is the probability that the 2nd ball is yellow or the 3rd ball is NOT yellow?
A) 1/2
B) 3/4
C) 5/6
D) 11/12
E) 1
Answer:
B
Source: GMAT Prep Now
First of all, it's useful to recognize that P(2nd ball is yellow or the 3rd ball is NOT yellow) is the SAME as P(1st ball is yellow or the 2nd ball is NOT yellow)
Let's apply the OR probability rule:
P(A or B) = P(A) + P(B) - P(A and B)
So, P(1st ball is yellow or the 2nd ball is NOT yellow) = P(1st ball is yellow) + P(2nd ball is NOT yellow) - P(1st ball is yellow AND the 2nd ball is NOT yellow)
P(1st ball is yellow) = 1/4
P(2nd ball is NOT yellow) = P(1st ball is NOT yellow) = 3/4
P(1st ball is yellow
AND the 2nd ball is NOT yellow) = P(1st ball is yellow)
x P(the 2nd ball is NOT yellow)
= 1/4
x 1
= 1/4
So, P(1st ball is yellow or the 2nd ball is NOT yellow) = P(1st ball is yellow) + P(2nd ball is NOT yellow) - P(1st ball is yellow AND the 2nd ball is NOT yellow)
= 1/4 + 3/4 - 1/4
= 3/4
= B
Cheers,
Brent
