Question

The Jones family was one of the first to come to the U.S. They had 4 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had:_______________.

(a) at least 3 girls
(b) at most 3 girls

Answer 1

a) The probability that the Jones family had at least 3 girls is 0.3125.

b) The probability that the Jones family had at most 3 girls is 0.9375.

Step-by-step explanation:

The probability that the Jones family had at least 3 girls is obtained below:

• From the given information, let X be the number of girls follows binomial distribution with number of trails 4 and probability of success is 0.5. Jones having four children. The 0.5 probability that having girl.

• That is, and p=0.50

• The probability mass function of X is ; P (X = x) = 4Cx X (0.5)^x X (1 - 0.5)^4-x

a) P(At least 3 girls) = P(3 girls) + P(4 girls)

= 4C3 x (0.5)^3 x (0.5)^1 + (0.5)^4

= 0.3125 is the probability that the Jones family had at least 3 girls

b) at most 3 girls ; The probability that the Jones family had at most 3 girls is obtained below:

• From the given information, let X be the number of girls follows binomial distribution with number of trails 4 and probability of success is 0.5. and .

• The probability mass function of X is, P (X = x) = 4Cx X (0.5)^x X (1 - 0.5)^4-x

• The required probability is P(x<=3) = 1 - P(X>3) = 1 - P(X = 4)

• = 1 - 0.0625

The probability that the Jones family had at most 3 girls is 0.9375.