Question

The Jones family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had: at least 4 girls? at most 3 girls?

Answer 1

Its a question on binomial distribution

Let X be the random variable which tracks the number of girls

P(at least 4 girls) = P(X=4) + P(X=5) + P(X=6)

= $_{4}^{6}\textrm{C}(0.5)^4*0.5^2 + _{5}^{6}\textrm{C}(0.5)^5*0.5^1 + _{6}^{6}\textrm{C}(0.5)^6*0.5^0$

= 0.344

P(at most 3 girls) = P(X=1) + P( X=2) + P(X=3)

= $_{1}^{6}\textrm{C}(0.5)^1*0.5^5 + _{2}^{6}\textrm{C}(0.5)^2*0.5^4 + _{3}^{6}\textrm{C}(0.5)^3*0.5^3$

= 0.656