Question

Suppose that njoman rolls a fair six-sided die and a fair four-sided die simultaneously. Let \[a\] be the event that the six-sided die lands on \[5\] and \[b\] be the event that the sum of the dice is \[7\]. Using the sample space of possible outcomes below, answer each of the following questions.

Answer 1

Event a has a probability of 1/6, while event b has a probability of 1/4 or 0.25.

Step-by-step explanation:

In this question, we have two events defined by rolling two dice simultaneously. Let event a be the event that the six-sided die lands on 5, and let event b be the event that the sum of the dice is 7.

To find the probability of event a, we need to determine how many outcomes satisfy event a divided by the total number of possible outcomes. Since we have one six-sided die, there are 6 possible outcomes, and only 1 outcome satisfies event a. Therefore, the probability of event a is 1/6.

Similarly, to find the probability of event b, we need to determine how many outcomes satisfy event b divided by the total number of possible outcomes. Since we have one six-sided die and one four-sided die, there are a total of 6 x 4 = 24 possible outcomes. Out of these 24 outcomes, there are 6 outcomes that satisfy event b (e.g., (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)). Therefore, the probability of event b is 6/24, which simplifies to 1/4 or 0.25.