33. Assuming a 1 : 1 sex ratio. what is the probability that three children from the same parents will consist of two daughters and one son?
(1) 0.375         (2) 0.125
(3) 0.675         (4) 0.75

Step-by-step solution

Assumptions

• Each child equally likely to be boy (B) or girl (G)
• P(B) = 1/2, P(G) = 1/2
• Sex of each child independent of others [web:79][web:88]

Count the arrangements

Sequences with 2 G and 1 B:

• G G B
• G B G
• B G G

There are 3 such permutations.

Probability of a specific arrangement

For example, G G B:

de>P(GGB) = (1/2) × (1/2) × (1/2) = 1/8

Each of the three sequences has probability 1/8.

Total probability

de>P(2 girls, 1 boy) = 3 × 1/8 = 3/8 = 0.375

So the correct option is 0.375 [web:79].

Why other options are wrong

• 0.125 (1/8): probability of one specific order (e.g., GGB), not all three
• 0.675: larger than 1/2, not compatible with binomial probabilities
• 0.75 (3/4): probability of “at least one daughter” or “at least one son”

Thus, the probability that three children consist of two daughters and one son is 0.375 (3/8).