JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Probability

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A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-

(A) $\frac{2}{9}$ ✓ Correct
(B) $\frac{1}{9}$
(C) $\frac{2}{27}$
(D) $\frac{1}{27}$

Answer: (A)

Solution

Let

P (tail) = p

. Since a head is twice as likely,

P (head) = 2 p

, and

p + 2 p = 1 \Rightarrow p = \frac{1}{3}

, so

P (head) = \frac{2}{3}

.

For 3 tosses, the probability of exactly 2 tails and 1 head is

(1 3) p^{2} (2 p) = 3 (\frac{1}{3})^{2} (\frac{2}{3}) = 3 \cdot \frac{1}{9} \cdot \frac{2}{3} = \frac{2}{9}

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Single correct option

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