1 In a family of 2 children what is the probability of havin

1. In a family of 2 children, what is the probability of having only 1 girl? (solve & explain)

2. In a family of 2 children, what is the probability of having at least 1 girl? (solve & explain)

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
p = probability of having = 1/2 = 0.50
a)
P( X = 1 ) = ( 2 1 ) * ( 0.5^1) * ( 1 - 0.5 )^1
= 0.5

b)
P( X < 1) = P(X=0)
= ( 2 0 ) * 0.5^0 * ( 1- 0.5 ) ^2
= 0.25
P( X > = 1 ) = 1 - P( X < 1) = 0.75