Question

Mary is rolling a standard six-sided die and spinning on a spinner with the number 1-8.

Answer 1

Answer:

a) Dice and spinner are different objects, with no relation between themselves, and thus her dice rolls and spinning outcomes are independent.

b) $\frac{1}{48}$ probability of her rolling a 4 and spinning an 8.

c) $\frac{1}{8}$ probability of her rolling an even number and spinning a number less than 3.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

A) Are her dice rolls and spinning outcomes independent or dependent?

Dice and spinner are different objects, with no relation between themselves, and thus her dice rolls and spinning outcomes are independent.

B) What is the probability of her rolling a 4 and spinning an 8?

Since the events are independent, we find each separate probability and multiply them.

Probability of rolling a 4:

One side out of 6 on the dice. So

$P(A) = \frac{1}{6}$

Probability of spinning an 8:

One side out of 8 on the spinner. So

$P(B) = \frac{1}{8}$

Probability of rolling a 4 and spinning an 8:

$P(A \cap B) = P(A)P(B) = \frac{1}{6} \times \frac{1}{8} = \frac{1}{48}$

$\frac{1}{48}$ probability of her rolling a 4 and spinning an 8.

C) What is the probability of her rolling an even number and spinning a number less than 3?

Since the events are independent, we find each separate probability and multiply them.

Probability of rolling an even number:

2, 4 or 6(3 sides out of 6). So

$P(A) = \frac{3}{6} = \frac{1}{2}$

Probability of spinning a number less than 3:

Two numbers(1 or 2) out of 8 on the spinner. So

$P(B) = \frac{2}{8} = \frac{1}{4}$

Probability of rolling an even number and spinning a number less than 3:

$P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$

$\frac{1}{8}$ probability of her rolling an even number and spinning a number less than 3.