Question

Assume each newborn baby has a probability of approximately 0.53 of being female and 0.47 of being male. For a family with four ​children, let Xequalsnumber of children who are girls. a. Identify the three conditions that must be satisfied for X to have the binomial distribution. b. Identify n and p for the binomial distribution. c. Find the probability that the family has two girls and two boys.

Answer 1

0.3723

Explanation:

Since the number of girls = X

Probability of girls p = 0.53

Probability of boys q = 0.47

Number of observation n = 4

A) conditions for binomial distribution are

1: The number of observations n must be fixed.

2: Each observation is independent. 3: Each observation represents one of two outcomes ("success" or "failure").

B) for the question n = 4

p (probability of success for girls) = 0.53

C) n=4, r (number of trials) = 2

Using binomial expansion

4C2 *(p)² *(q)² = 6* (0.53)² * (0.47)²

= 0.3723

Therefore, the probability of the family having two boys and two girls is 0.3723.