Question

Five coins are tossed 3200 times. The expected number of times we get exactly two heads is

Answer 1

in case of each coin,

probability to get head = probability to get tail = 1/2

Let P(Head) = p = 1/2 and P(Tail) = q = 1/2

now applying binomial probability distribution to get the expected number of heads as follows :

expected number of heads = $N.^nC_r(p)^r(q)^{(n-r)}$

for exactly two heads,

r = 2, n = 5 , N = 3200, p = 1/2 and q = 1/2

so, number of expected heads = $3200.^5C_2(1/2)^2(1/2)^{(5-2)}$

= 3200 × (5!/2! × 3!) × (1/2)^5

= 3200 × (120/12) × 1/32

= 1000

hence, 1000 times we get exactly two heads when we tossed 5 coins 3200 times.