what is the probability of picking a blue marble and rolling an odd number? write your answer as a fraction…

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.

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.

Answer

Explanation:

Step1: Calculate probability of picking blue marble

There are 3 blue marbles and 9 total marbles. Probability $P(\text{blue})=\frac{3}{9}=\frac{1}{3}$.

Step2: Calculate probability of rolling odd - number

A die has 6 sides, and 3 odd numbers (1, 3, 5). Probability $P(\text{odd})=\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since picking a marble and rolling a die are independent events, $P(\text{blue and odd})=P(\text{blue})\times P(\text{odd})$. $P(\text{blue and odd})=\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$