JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Probability

Each of the persons

A

and

B

independently tosses three fair coins. The probability that both of them get the same number of heads is:

Answer: (A)

Solution

When tossing 3 fair coins, the probability of getting exactly

k

heads is

P (k) = (k 3) (\frac{1}{2})^{3} = \frac{( k 3 )}{8}

.

For 0 heads:

P (0) = \frac{1}{8}

For 1 head:

P (1) = \frac{3}{8}

For 2 heads:

P (2) = \frac{3}{8}

For 3 heads:

P (3) = \frac{1}{8}

The probability that both

A

and

B

get the same number of heads:

P = P (0)^{2} + P (1)^{2} + P (2)^{2} + P (3)^{2}

= (\frac{1}{8})^{2} + (\frac{3}{8})^{2} + (\frac{3}{8})^{2} + (\frac{1}{8})^{2}

= \frac{1 + 9 + 9 + 1}{64} = \frac{20}{64} = \frac{5}{16}

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Single correct option