JEE Main 2021 — Probability Question with Solution

Let x be the number of heads obtained by A, and y be the number of heads obtained by B.

Note that x and y are binomial variable with parameters n = 3 and p = $$\frac{1}{2}$$

$$\therefore$$ Probability that both A and B obtained the same number of heads is

$$=P(x=0).P(y=0)+P(x=1).P(y=1)+P(x=2).P(y=2)+P(x=3).P(y=3)$$

$$={\left[3_{C_0}{\left(\frac{1}{2}\right)}^3\right]}^2+{\left[3_{C_1}{\left(\frac{1}{2}\right)}^3\right]}^2+{\left[3_{C_2}{\left(\frac{1}{2}\right)}^3\right]}^2+{\left[3_{C_3}{\left(\frac{1}{2}\right)}^3\right]}^2$$

$$={\left(\frac{1}{2}\right)}^6\left[1+9+9+1\right]$$

$$=\frac{20}{64}$$

$$=\frac{5}{16}$$