Probability — Easy JEE math MCQ
A bag contains $5$ red balls and $3$ blue balls. Two balls are drawn at random without replacement. The probability that both balls are red is:
- A. $\frac{5}{14}$
- B. $\frac{10}{28}$
- C. $\frac{25}{64}$
- D. $\frac{5}{8}$
Solution
Total balls = $5 + 3 = 8$
Probability of first ball being red = $\frac{5}{8}$
After drawing one red ball, remaining red balls = $4$, total balls = $7$
Probability of second ball being red = $\frac{4}{7}$
Probability of both balls being red:
$$P = \frac{5}{8} \times \frac{4}{7} = \frac{20}{56} = \frac{5}{14}$$