A coin is tossed 5 times. The probability of head is \(\frac{1}{2}\). The probability of exactly 2 heads is

Concept:

Binomial distribution:

It gives the probability of happening of event 'r' times exactly in 'n' trials.

P(r) = ⁿC_r(p)^r(q)^{n - r}

where n = number of trials, r = number of favourable events, p = probability of happening of an event and q = (1 - p) probability of not happening of an event.

Calculation:

Given:

n = 5 (tossed 5 times), r = 2 (exactly two heads), p = 1/2 (probability of happening event) and q = 1/2 (probability of not happening of an event)

P(r) = nCr(p)r(q)n - r

∴ probability of head occurring exactly 2 times is P(2).

\(P(2)={5_{{C_2}}}\left(\frac{1}{2}\right)^2\left(\frac{1}{2}\right)^3\Rightarrow\frac{5}{16}\)