A family has 4 children Draw a tree diagram and list the sam

A family has 4 children. Draw a tree diagram and list the sample space showing all of the possible arrangements of the sex of the children. (5 pts. for tree, 5 pts. for sample space) B. Determine the following probabilities: (Write your answer as a fraction.) 1) all children are girls 2) at least one child is a girl 3) There are only 2 boys given the first child is a girl

Solution

a)
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

a)
P( Boy) = P( Girl) = 0.5
P( X = 4 ) = ( 4 4 ) * ( 0.5^4) * ( 1 - 0.5 )^0
= 0.0625

b)
P( X < 1)   = P(X=0)         
= ( 4   0 ) * 0.5^0 * ( 1- 0.5 ) ^4         
= 0.0625

P( X > = 1 ) = 1 - P( X < 1) = 0.9375