Final answer:
To calculate the probability that in a family with 4 children there are exactly three daughters, we can use the binomial probability formula.
Step-by-step explanation:
To calculate the probability that in a family with 4 children there are exactly three daughters, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) imes p^k imes (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success on each trial
- n is the number of trials
- k is the number of successes
In this case, p (the probability of having a daughter) is 0.48, n (the number of children) is 4, and k (the desired number of daughters) is 3. Plugging in these values, we get:
P(X = 3) = C(4, 3) imes 0.48^3 imes (1-0.48)^(4-3)
Using the combination formula C(n, k) = n! / (k! imes (n-k)!), the calculation becomes:
P(X = 3) = 4! / (3! imes (4-3)!) imes 0.48^3 imes (1-0.48)^(4-3)