Question

In a family with eight children, what is the probability that exactly six are boys?

Options:
a. 0.273
b. 0.109
c. 0.164
d. 0.219

Answer 1

The probability of having exactly six boys in a family of eight children, assuming an equal chance of having a boy or a girl, is approximately 0.109, which corresponds to option b. 0.109.

Step-by-step explanation:

The subject of this question is Mathematics, specifically dealing with probability. To find the probability of having exactly six boys in a family of eight children, we can use the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n' is the total number of trials (or children, in this case), 'k' is the number of successes (boys), and 'p' is the probability of a success on any given trial.

Assuming that the likelihood of having a boy is 1/2 (or 0.5) and a girl is also 1/2, simply because there are two genders and we are not given any information to sway the probability from being equal, we can calculate:

P(X = 6) = (8 choose 6) * (0.5)^6 * (0.5)^(8-6)

P(X = 6) = 28 * (0.5)^6 * (0.5)^2

P(X = 6) = 28 * (0.015625) * (0.25)

P(X = 6) = 28 * 0.00390625

P(X = 6) = 0.109375, which is approximately option b. 0.109.