Question

what is the probability of picking an orange marble and rolling an even number? write your answer as a fraction or a whole number. with fractions, use a slash (/) to separate the numerator and denominator.

Explanation:

Step1: Calculate the probability of picking an orange marble

There are 4 orange marbles and a total of 9 marbles. The probability of picking an orange marble is the number of orange marbles divided by the total number of marbles. So, \(P(\text{orange})=\frac{4}{9}\).

Step2: Calculate the probability of rolling an even number on a die

A die has 6 faces numbered from 1 - 6. The even - numbered faces are 2, 4, 6. So there are 3 even - numbered faces. The probability of rolling an even number is \(P(\text{even})=\frac{3}{6}=\frac{1}{2}\).

Step3: Use the multiplication rule for independent events

Since picking a marble and rolling a die are independent events, the probability of both events occurring is the product of their individual probabilities. \(P = \frac{4}{9}\times\frac{1}{2}\).

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Answer:

\(\frac{2}{9}\)