Final answer:
To find the outcomes in event F or G, we list the outcomes that are either in F, in G, or in both. The outcomes in F or G are {10, 11, 12, 13, 14, 15, 16, 17}. We can find P(F or G) by counting the number of outcomes in F or G and dividing by the total number of outcomes in the sample space. The probability is 2/3. We can also use the general addition rule to find P(F or G) by adding the probabilities of F and G and subtracting the probability of F and G intersecting.
Step-by-step explanation:
To find the outcomes in event F or G, we need to find the outcomes that are either in F, in G, or in both. The outcomes in event F are {10, 11, 12, 13, 14} and the outcomes in event G are {14, 15, 16, 17}. The outcomes that are in either F or G are {10, 11, 12, 13, 14, 15, 16, 17}.
To find P(F or G) by counting the number of outcomes, we divide the number of outcomes in F or G by the total number of outcomes in the sample space. The number of outcomes in F or G is 8 and the total number of outcomes in the sample space is 12. Therefore, P(F or G) = 8/12 = 2/3.
To find P(F or G) using the general addition rule, we add the probabilities of F and G and subtract the probability of F and G intersecting. The probability of F is 5/12, the probability of G is 4/12, and the probability of F and G intersecting is 1/12. Therefore, P(F or G) = P(F) + P(G) - P(F and G) = 5/12 + 4/12 - 1/12 = 8/12 = 2/3.