Answer to Question #208322 in Statistics and Probability for Humphrey

Question

Assume that the probability of a male birth is 1/2. Find the probability that in a family of 4 children there will be:

a) at least 1 boy and at least 1 girl. 

Answer 1

$P(0\; boy)=0.5^4=0.0625.$

$P(0\;girl)=0.5^4=0.0625.$

$P( at\;least\;1\;boy\;and\;at\;least\;1\;girl)=1-P(0\;boy)-P(0\;girl)=$

$=1-0.0625-0.0625=0.875.$