Question

A fair tossed 10 times . Find the probability of obtaining (i) exactly four heads (ii) 3 heads and 7 tails (iii) at least one head

Answer 1

0.205 ; 0.117 ; 0.999

Explanation:

Using binomial probability distribution :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Probability of success, p = 0.5

P(x = 4) = 10C4 * 0.5^4 * 0.5^6

P(X = 4) = 0.205078125

B.) 3 heads and 7 tails

P(X = 7) = 10C7 * 0.5^7 * 0.5^3

P(X = 7) = 120 * 0.0009765625

P(X = 7) = 0.117

P(atleast one head)

P(x greater than equal to 1) = p(x =1) +... P(x = 10)

Using a binomial probability calculator :

P(x greater than equal to 1) = 0.999