Let the random variable X represent the positive difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. Then probability \(P(X \le 3)\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25/32
Let H be the number of heads. The number of tails is 6 − H, so
\(X = |H - (6 - H)| = |2H - 6|\)
For H = 0, 1, 2, 3, 4, 5, 6 this gives X = 6, 4, 2, 0, 2, 4, 6. So
\(X \le 3 \iff X = 0 \text{ or } 2 \iff H = 2, 3, 4\)
H follows the binomial distribution with n = 6 and p = 1/2:
\( \displaystyle P(X \le 3) = \frac{^{6}C_{2} + {^{6}C_{3}} + {^{6}C_{4}}}{2^6} \)
\( \displaystyle = \frac{15 + 20 + 15}{64} = \frac{50}{64} = \frac{25}{32} \)