Question

the tree diagram shows the outcomes of rolling a die and flipping a coin.
what is the probability of rolling an even number and flipping a head?

Explanation:

Step1: Determine the number of favorable outcomes

When rolling a die, the even numbers are \(2\), \(4\), \(6\) (3 outcomes). When flipping a coin, getting heads is 1 outcome. By the multiplication principle, the number of favorable outcomes (even - number and heads) is \(3\times1 = 3\).

Step2: Determine the total number of outcomes

When rolling a die, there are \(6\) outcomes. When flipping a coin, there are \(2\) outcomes. By the multiplication principle, the total number of outcomes is \(6\times2=12\).

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P = \frac{3}{12}\).

Answer:

\(\frac{3}{12}\)