Question

Assumjng that boy and girl babies are equally likely, what would be kathys probability of having exactly four daughters if she were to have four children altogether? Answer must be a fraction or interger.

Answer 1

The probability of Kathy having four daughters out of four children is 1/16, calculated as (1/2)^4 since each child being a girl is an independent event with a probability of 1/2.

Step-by-step explanation:

The probability of Kathy having exactly four daughters when she has four children altogether, assuming that boy and girl babies are equally likely, can be calculated using the concept of binomial probability. Since each child is an independent event, the chance of having a daughter is 1/2. To have four daughters in four tries, we calculate (1/2) × (1/2) × (1/2) × (1/2).

The calculation is as follows:

• P(first child is a daughter) = 1/2
• P(second child is a daughter) = 1/2
• P(third child is a daughter) = 1/2
• P(fourth child is a daughter) = 1/2

Multiplying these probabilities together gives us:

(1/2) x (1/2) x (1/2) x (1/2) = 1/16

Therefore, the probability of Kathy having exactly four daughters is 1/16.