Assume that male and female births are equally likely and that the birth of any child does not affect theprobability of the gender of any other children. Find the probability of at most three girls in ten births.
A) 0.172
B) 0.300
C) 0.003
D) 0.333

Question

Quizplus · Accepted Answer

The probability of at most three girls in ten births can be calculated using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials (births), k is the number of successful outcomes (girls), and p is the probability of success on each trial (0.5 for girls, since male and female births are equally likely). We need to calculate this for k = 0, 1, 2, and 3, and sum those probabilities.P(0 girls) + P(1 girl) + P(2 girls) + P(3 girls) = (10 choose 0) * 0.5^0 * 0.5^10 + (10 choose 1) * 0.5^1 * 0.5^9 + (10 choose 2) * 0.5^2 * 0.5^8 + (10 choose 3) * 0.5^3 * 0.5^7.Calculating these values and summing them gives a probability of approximately 0.172, which matches choice A.

Assume That Male and Female Births Are Equally Likely and That