Question

A number cube has the numbers 1, 2, 5, 5, 6, and 6 on its faces. Match the probability with the outcome. 1. P(4) 2. P(5 ∪ 6) 3. P(1 ∪ 2) 4. 0 P(2 ∪ 5 ∪ 6)

Answer 1

To match the probability with an outcome on a non-standard dice cube with the numbers 1, 2, 5, 5, 6, and 6, probabilities are calculated based on the faces available. P(4) is 0, P(5 ∪ 6) is 0.67, P(1 ∪ 2) is 0.33, and P(2 ∪ 5 ∪ 6) is also 0.67.

Step-by-step explanation:

The question involves calculating probabilities associated with the outcomes of rolling a number cube that does not have all six different numbers on its faces. We will match each probability to the corresponding outcome:

1. P(4) - This is the probability of rolling a 4. However, the number cube does not have a 4 on any of its faces, thus P(4) = 0.
2. P(5 ∪ 6) - This represents the probability of rolling either a 5 or a 6. Since there are two 5s and two 6s on the cube, P(5 ∪ 6) = 4/6 or about 0.67.
3. P(1 ∪ 2) - This is the probability of rolling either a 1 or a 2. With one 1 and one 2 on the cube, P(1 ∪ 2) = 2/6 or approximately 0.33.
4. The symbol ∪ represents the union of events, so P(2 ∪ 5 ∪ 6) is actually the probability of rolling a 2, 5, or 6, which we already found to be 4/6, since there are four faces among six that have these numbers.