Question

A couple plans to have four children. Using a tree diagram , obtain the sample space. Then, find the probability that the family has no boys.

Answer 1

Use b for boy and g for girl.

This is the resultant combinations:

b b b b
b b b g

b b g b
b b g g

b g b b
b g b g

b g g b
b g g g

g b b b
g b b g

g b g b
g b g g

g g b b
g g b g

g g g b
g g g g

If you count all the possibilities they are 16. Which is the same as 2^4 = 2*2*2*2, so I know that I didn't miss a combination.

The possibility of having no boys is one (g g g g combination) in 16, so the probability is 1 / 16 = 0,0625.