Question

DEPENDENT EVENTS AND CONDITIONAL PROBABILITY A bucket contains 12 balls, 8 of which are white. If you reach in and randomly grab two balls one at a time without replacement, what is the probability that both are white? •Enter your answer as a fraction in lowest terms.

Answer 1

Answer:

The probability that both are white is;

$\frac{14}{33}$

Explanation:

We want to find the probability that both balls removed without replacement are white.

$P=P_1\times P_2$

Where;

$\begin{gathered} P_1=\text{ probability that the first ball is white} \\ P_2=\text{ Probability that the second ball is white} \end{gathered}$

Solving for the first;

$\begin{gathered} P_1=\frac{\text{Number of white balls}}{\text{Total number of balls}}=\frac{8}{12} \\ P_1=\frac{2}{3} \end{gathered}$

For the second selection, since there is no replacement, the number of white balls would have reduced by one to 7 and the total number of balls will also reduce to 11.

So we have;

$P_2=\frac{7}{11}$

So;

$\begin{gathered} P=P_1\times P_2 \\ P=\frac{2}{3}\times\frac{7}{11} \\ P=\frac{14}{33} \end{gathered}$

Therefore, the probability that both are white is;

$\frac{14}{33}$