Question

A bottle contains many balls with different colors. Two balls arechosen without replacement. The probability of selecting agreen ball and then a white ball is 0.15, and the probability ofselecting a green ball on the first draw is 0.65. What is theprobability of selecting a white ball on the second draw, giventhat the first ball drawn was green?Enter your answer as a decimal rounded to the nearesthundredth.

Answer 1

We have to find the probability of selecting a white ball on the second draw given that the first ball drawn was green.

We know that probability of selecting a green ball and then a white ball without replacement is 0.15, so we can write:

$P(G,W)=0.15$

We also know that the probability of selecting a green ball in the first draw is 0.65:

$P(G)=0.65$

Then, we can use this to find the conditional probability of selecting a white ball on the second draw given that the first ball drawn was green can be calculated as:

$P(W|G)=\frac{P(G,W)}{P(G)}=\frac{0.15}{0.65}\approx0.231$

Answer: the probability is 0.231.