Question

use the tree diagram to find the probability of tossing a head first an then a tail when a coin is tossed twice.

Explanation:

Step1: Determine the probability of each toss

The probability of getting a head (\(H\)) in a single coin toss is \(P(H)=\frac{1}{2}\), and the probability of getting a tail (\(T\)) in a single coin toss is \(P(T)=\frac{1}{2}\).

Step2: Use the multiplication rule for independent events

Since the two coin - tosses are independent events, the probability of getting a head first and then a tail is \(P(H\cap T)=P(H)\times P(T)\).
Substitute \(P(H)=\frac{1}{2}\) and \(P(T)=\frac{1}{2}\) into the formula: \(P(H\cap T)=\frac{1}{2}\times\frac{1}{2}\).

Answer:

\(\frac{1}{4}\)