Question

assuming that boy and girl babies are equally likely, what would be kathys probability of having at least one daughter if she were to have four children altogether? (you may want to use a tree diagram to construct the sample space.) the probability is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine total outcomes

Each child has 2 genders (boy/girl), so for 4 children, total outcomes = \(2^4 = 16\).

Step2: Find unfavorable outcomes

Unfavorable (no daughters, all boys): Only 1 outcome (BBBB).

Step3: Calculate favorable outcomes

Favorable (at least 1 daughter) = Total - Unfavorable = \(16 - 1 = 15\).

Step4: Compute probability

Probability = \(\frac{\text{Favorable}}{\text{Total}} = \frac{15}{16}\).

Answer:

\(\frac{15}{16}\)