Question

1. a nickel is tossed, a number - cube with faces labeled 1 - 6 is rolled, and a quarter is tossed. what is the probability that the nickel lands on heads, the number cube shows an odd number, and the quarter lands on tails?

a. $\frac{1}{2}$
b. $\frac{3}{10}$
c. $\frac{1}{6}$
d. $\frac{1}{8}$

Explanation:

Step1: Find probability of nickel landing on heads

A nickel has 2 sides (heads and tails), so the probability of it landing on heads, $P(N_{H})=\frac{1}{2}$.

Step2: Find probability of number - cube showing an odd number

A number cube labeled 1 - 6 has 3 odd numbers (1, 3, 5) out of 6 possible outcomes. So the probability, $P(C_{O})=\frac{3}{6}=\frac{1}{2}$.

Step3: Find probability of quarter landing on tails

A quarter has 2 sides (heads and tails), so the probability of it landing on tails, $P(Q_{T})=\frac{1}{2}$.

Step4: Use the multiplication rule for independent events

Since the events are independent, the probability of all three events occurring is $P = P(N_{H})\times P(C_{O})\times P(Q_{T})$. Substitute the values: $P=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$.

Answer:

D. $\frac{1}{8}$