Question

The Wilson family had 8 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had:

at least 4 girls?

at most 5 girls?

round to 4 place decimal accuracy

Answer 1

Let x denote number of girls in n= 8 children

p=0.5

1-p =0.5

X~ Binomial ( n=8, p=0.5)

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

A)

P(atleast 4 girls)

= 1 -[ p(0) +p(1) +p(2)+p(3)]

= 1 - [ 8C0 * 0.5^0 * 0.5^8 +8C1 * 0.5^1 * 0.5^7 + 8C2 * 0.5^2 * 0.5^6+ 8C3 * 0.5^3 *0.5^5]

= 1 - [ 0.0039 + 0.0312 + 0.1094+0.2187 ]

= 1- 0.3632

= 0.6368

B)

P(at most 5 girls)

= P(0) +p(1)+p(2)+p(3)+p(4)+p(5)

= 8C0 * 0.5^0 * 0.5^8 +8C1 * 0.5^1 * 0.5^7 +8C2 * 0.5^2 * 0.5^6+

8C3 * 0.5^3 * 0.5^5 +8C4 * 0.5^4 * 0.5^4+8C5 * 0.5^5 * 0.5^3

=0.0039+0.0312+0.1094 + 0.2187 +0.2734 + 0.2187

=0.8553