Question

The probability of choosing two green balls without replacement is 111, and the probability of choosing one green ball is 13.What is the probability of drawing a second green ball, given that the first ball is green?

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given probabilities

$\begin{gathered} Pr(2\text{ greens\rparen}=\frac{1}{11} \\ Pr(one\text{ green\rparen}=\frac{1}{3} \end{gathered}$

STEP 2: Write the probability formula for probability of second green given first green

$\begin{gathered} Pr(G2|G1)=\frac{Pr(2\text{ greens\rparen}}{Pr(one\text{ green\rparen}} \\ =\frac{1}{\frac{11}{\frac{1}{3}}}=\frac{1}{11}\div\frac{1}{3}=\frac{1}{11}\times\frac{3}{1}=\frac{3}{11} \end{gathered}$

Hence, the answer is 3/11