Question

three coins are flipped. the possible results are shown in the tree diagram below. what is p(2 heads, 1 tails)?

Explanation:

Step1: Count total outcomes

There are 8 total possible outcomes from flipping 3 coins as shown in the tree - diagram: (H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T).

Step2: Count favorable outcomes

The favorable outcomes (2 heads and 1 tails) are (H, H, T), (H, T, H), (T, H, H), so there are 3 favorable outcomes.

Step3: Calculate probability

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(2\text{ heads}, 1\text{ tails})=\frac{3}{8}$.

Answer:

$\frac{3}{8}$