Question

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

Explanation:

Step1: Calculate total number of balls

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

Step2: Calculate number of ways to choose 2 black balls

Number of ways to choose 2 black balls from 5 is given by combination formula \( C(n, k) = \frac{n!}{k!(n - k)!} \), where \( n = 5 \), \( k = 2 \). So \( C(5, 2) = \frac{5!}{2!(5 - 2)!} = \frac{5\times4}{2\times1} = 10 \).

Step3: Calculate total number of ways to choose 2 balls

Total number of ways to choose 2 balls from 7 is \( C(7, 2) = \frac{7!}{2!(7 - 2)!} = \frac{7\times6}{2\times1} = 21 \).

Step4: Calculate probability

Probability = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{10}{21} \).

Answer:

\(\frac{10}{21}\) (corresponding to the option with \( \boldsymbol{\frac{10}{21}} \))