Question

Amber has a bag of $24$ marbles. $7$ marbles are red, $5$ marbles are blue, and the rest are pink. James takes out two marbles without replacing them. What is the probability that they are both blue?

• A. $\frac{5}{24}$
• B. $\frac{5}{138}$
• C. $\frac{5}{144}$
• D. $\frac{25}{576}$

Answer 1

The correct option is B

$\frac{5}{138}$

Explanation for correct option:
Given that bag has $24$ marbles of which $7$ marbles are red, $5$ marbles are blue, and the rest are pink

Probability of an event $=\frac{n_f}{n_T}$where $n_f,n_T$ are number of favorable outcomes and total number of outcomes respectively
Probability of drawing one marble that is blue $=\frac{5}{24}$
Probability of drawing another marble that is blue $=\frac{4}{23}$
Probability that both marble are blue $=\frac{5}{24}\times \frac{4}{23}$
$=\frac{5}{138}$

Hence, option (B) is correct.