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

what is the probability of picking a purple 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 purple 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 purple marble

There is 1 purple marble and a total of 1 + 7=8 marbles. So the probability of picking a purple marble $P(purple)=\frac{1}{8}$.

Step2: Calculate probability of rolling an odd - number

A standard die has 6 sides, and the odd - numbers are 1, 3, 5. So there are 3 odd - numbers. The probability of rolling an odd number $P(odd)=\frac{3}{6}=\frac{1}{2}$.

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 $P = P(purple)\times P(odd)$. Substitute the values: $P=\frac{1}{8}\times\frac{1}{2}=\frac{1\times1}{8\times2}=\frac{1}{16}$.

Answer:

$\frac{1}{16}$