Question

a box contains 5 black and 2 white balls. 2 balls are drawn without replacement. find the probability of drawing 2 white balls.

Explanation:

Step1: Find total number of balls

Total balls = 5 (black) + 2 (white) = 7.

Step2: Probability of first white ball

Probability of drawing first white ball = $\frac{2}{7}$.

Step3: Probability of second white ball (without replacement)

After drawing one white ball, remaining white balls = 1, total balls = 6. Probability of second white ball = $\frac{1}{6}$.

Step4: Multiply probabilities (for two events)

Probability of two white balls = $\frac{2}{7} \times \frac{1}{6} = \frac{2}{42} = \frac{1}{21}$.

Answer:

$\frac{1}{21}$ (corresponding to the option with $\boldsymbol{\frac{1}{21}}$)