Question

in a single experiment, a die is tossed and a spinner with the letters a, b, and c is spun. each letter is equally likely. find the sample space and then find the probability of getting a 2 on the die and a b on the spinner.
a. the sample space is 18. the probability of getting 2 and b is $\frac{1}{18}$.
b. the sample space is 9. the probability of getting 2 and b is $\frac{1}{9}$.
c. the sample space is 18. the probability of getting 2 and b is $\frac{1}{9}$.
d. the sample space is 9. the probability of getting 2 and b is $\frac{1}{18}$.

Explanation:

Step1: Calculate sample - space size

A die has 6 faces and a spinner has 3 letters. By the multiplication principle, the size of the sample space $n(S)=6\times3 = 18$.

Step2: Calculate probability

The event of getting a 2 on the die and a B on the spinner is one specific outcome. Let $E$ be the event. The probability $P(E)=\frac{n(E)}{n(S)}$, where $n(E) = 1$ and $n(S)=18$. So $P(E)=\frac{1}{18}$.

Answer:

A. The sample space is 18. The probability of getting 2 and B is $\frac{1}{18}$