Question

what is the probability of picking a blue marble and rolling an odd 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 a blue marble

There are 5 blue marbles and 2 purple marbles, so the total number of marbles is \(5 + 2=7\). The probability of picking a blue marble \(P(\text{blue})=\frac{5}{7}\).

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

A die has 6 faces numbered from 1 - 6. The odd - numbered faces are 1, 3, 5. So the probability of rolling an odd number \(P(\text{odd})=\frac{3}{6}=\frac{1}{2}\).

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 \(P = P(\text{blue})\times P(\text{odd})\). Substitute the values: \(P=\frac{5}{7}\times\frac{1}{2}=\frac{5\times1}{7\times2}=\frac{5}{14}\).

Answer:

\(\frac{5}{14}\)