Final answer:
a. The probability is 0.45. b. The probability is 0.33. c. The probability is 0.0875. d. The probability is 0.875.
Step-by-step explanation:
a. To find the probability that a randomly selected piece of equipment is a Moderate item or that it is in working order, we need to add the probabilities of the two events happening. From the contingency table, we can see that the probability of a Moderate item is 0.10 and the probability of being in working order is 0.35. Therefore, the probability is 0.10 + 0.35 = 0.45.
b. To find the probability that a randomly selected piece of equipment is a high-use item given that it is in working order, we need to divide the number of high-use items in the working order category by the total number of items in the working order category. From the contingency table, we can see that there are 20 high-use items in working order and a total of 60 items in working order. Therefore, the probability is 20/60 = 1/3 = 0.33.
c. To find the probability that a randomly selected piece of equipment is a low-use item and it is in working order, we need to multiply the probabilities of the two events happening. From the contingency table, we can see that the probability of a low-use item is 0.25 and the probability of being in working order is 0.35. Therefore, the probability is 0.25 * 0.35 = 0.0875.
d. To find the probability that a randomly selected piece of equipment is in working order given that it is a low-use item, we need to divide the number of low-use items in the working order category by the total number of low-use items. From the contingency table, we can see that there are 7 low-use items in working order and a total of 8 low-use items. Therefore, the probability is 7/8 = 0.875.