Question

8. In a game, a player must spin a spinner and roll a number cube. The spinner has four congruent sections and the sections are labeled 1, 2, 3, and 4. The number cube has six congruent faces and the faces are labeled 1, 2, 3, 4, 5, and 6. What is the probability of a player spinning a 4 and then rolling a 4?

Answer 1

The probability of spinning a 4 and then rolling a 4 is calculated by multiplying the individual probabilities of each event, resulting in a combined probability of 1/24, or 0.0417 when rounded to four decimal places.

Step-by-step explanation:

To determine the probability of a player spinning a 4 and then rolling a 4, we need to consider the probability of each independent event and then multiply them together. Since the spinner has 4 congruent sections numbered 1 through 4, the probability of spinning a 4 is 1 out of 4, or ¼. Similarly, the number cube has 6 faces, so the probability of rolling a 4 is 1 out of 6, or ⅗.

To find the combined probability of both events occurring, we multiply the probabilities of the separate events:

P(spinning a 4 and rolling a 4) = P(spinning a 4) × P(rolling a 4) = ¼ × ⅗

Now, we can calculate the probability:

P(spinning a 4 and rolling a 4) = ¼ × ⅗ = ⅔×6 = ⅔×6 = 1/24

Therefore, the probability of spinning a 4 and then rolling a 4 is 1/24, which can be rounded to four decimal places as 0.0417.