JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Probability

WhatsApp Email

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the number of tosses of the coin, then the mean of

X

(A) $\frac{21}{16}$ ✓ Correct
(B) $\frac{81}{64}$
(C) $\frac{15}{16}$
(D) $\frac{37}{16}$

Answer: (A)

Solution

Given

P (H) = \frac{3}{4}

and

P (T) = \frac{1}{4}

. The random variable

X

can take values 1, 2, or 3.

P (X = 1) = P (H) = \frac{3}{4}

P (X = 2) = P (T H) = \frac{1}{4} \cdot \frac{3}{4} = \frac{3}{16}

P (X = 3) = P (T T H) + P (T T T) = \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{3}{4} + (\frac{1}{4})^{3} = \frac{3}{64} + \frac{1}{64} = \frac{1}{16}

. Mean

E (X) = 1 \cdot \frac{3}{4} + 2 \cdot \frac{3}{16} + 3 \cdot \frac{1}{16} = \frac{3}{4} + \frac{3}{8} + \frac{3}{16} = \frac{21}{16}

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Probability →

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Probability

Solution

More JEE Main questions on Probability