Question

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

Explanation:

Step1: Count total outcomes

Total number of outcomes when flipping 3 coins is \(2\times2\times2 = 8\) (using the multiplication principle, 2 choices - head or tail - for each coin flip).

Step2: Count favorable outcomes

The favorable outcomes (2 heads and 1 tail) are \((H,H,T)\), \((H,T,H)\), \((T,H,H)\). So there are 3 favorable outcomes.

Step3: Calculate probability

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

Answer:

\(\frac{3}{8}\)