Respuesta :
Answer:
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.
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.
