Question

Find the probability that when a couple has three children, at least one of themis a girl. (Assume that boys and girls are equally likely.)

Answer 1

Answer:   $\bold{\dfrac{7}{8}=87.5\%}$

Step-by-step explanation:

"At least one girl" means P(1 girl) + P(2 girls) + P(3 girls)   or   1 - P(all boys)

I will use the latter: 1 - P(all boys)

P(all boys) = $\dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2}=\dfrac{1}{8}$

$1 - P(all\ boys) \quad = \quad 1-\dfrac{1}{8}\quad =\large\boxed{\dfrac{7}{8}}$