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 $P(X ≤ 3)$ is equal to.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25/32
Let X = |H − T| for 6 tosses.
Since H + T = 6,
$X = |2H - 6|$
Requirement:
$X \le 3 \Rightarrow |2H - 6| \le 3$
$-3 \le 2H - 6 \le 3$
$3 \le 2H \le 9$
$1.5 \le H \le 4.5$
Thus possible integer values of H: 2, 3, 4
Total outcomes = 64
Favourable outcomes:
H = 2 ⇒ number of ways = 15
H = 3 ⇒ number of ways = 20
H = 4 ⇒ number of ways = 15
Total favourable = 15 + 20 + 15 = 50
Probability:
$P(X \le 3) = \frac{50}{64} = \frac{25}{32}$