Question

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

Explanation:

Step1: Determine total number of outcomes

From the tree - diagram, the total number of possible outcomes when three coins are flipped is \(n = 8\).

Step2: Count favorable outcomes

The favorable outcomes for getting 2 heads and 1 tail are \((H,H,T)\), \((H,T,H)\), \((T,H,H)\). So the number of favorable outcomes \(m=3\).

Step3: Calculate probability

The probability formula is \(P=\frac{m}{n}\). Substituting \(m = 3\) and \(n = 8\), we get \(P=\frac{3}{8}\).

Answer:

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