Question

A biased coin is tossed 4 times. The probability of heads on any toss is 0.4. Let X denote the number of heads that come up. Calculate: (i) ( ≤ 2) (ii) (1 ≤ ≤ 3)

Answer 1

0.8208 ; 0.8448

Explanation:

Given the following :

Number of tosses = 4

Probability of head on any toss :

P(head) = 0.4

Therefore ;

(1 - p(head)) = (1 - 0.4) = 0.6

Binomial probability :

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

Where:

n = number of trials ; x = number of success ; P = probability of success.

P(X≤2) = P(0) + P(1) + p(2)

using binomial probability calculator to ensure faster computation:

P(X≤2) = 0.1296 + 0.3456 + 0. 3456

= 0.8208

B)

P(1 ≤ X ≤ 3) = P(1) + P(2) + P(3)

P(1 ≤ X ≤ 3) = 0.3456 + 0.3456 + 0.1536

= 0.8448