what is the probability of picking a purple marble and rolling an even number? write your answer as a…

what is the probability of picking a purple 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.

what is the probability of picking a purple 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.

Answer

Explanation:

Step1: Calculate probability of picking purple marble

There are 9 marbles in total and 3 purple marbles. So the probability of picking a purple marble $P(purple)=\frac{3}{9}=\frac{1}{3}$.

Step2: Calculate probability of rolling an even - number

A standard die has 6 sides, and the even numbers are 2, 4, 6. So the probability of rolling an even number $P(even)=\frac{3}{6}=\frac{1}{2}$.

Step3: Calculate the combined probability

Since the two events are independent, the probability of both events occurring is the product of their individual probabilities. So $P(purple\ and\ even)=P(purple)\times P(even)=\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$