Answer: (a) The probability of being male or being a nursing major is the sum of the probabilities of being male and being a nursing major, minus the probability of being both male and a nursing major (since this intersection is counted twice):
P(being male or being nursing major) = P(male) + P(nursing major) - P(male and nursing major)
From the table, we have:
P(male) = 1110/3538 ≈ 0.314
P(nursing major) = 1016/3538 ≈ 0.287
P(male and nursing major) = 94/3538 ≈ 0.027
Therefore:
P(being male or being nursing major) ≈ 0.314 + 0.287 - 0.027 ≈ 0.574
Rounded to the nearest thousandth as needed, the probability of being male or being a nursing major is approximately 0.574.
(b) The probability of being female or not a nursing major is the sum of the probabilities of being female and not a nursing major:
P(being female or not being a nursing major) = P(female) + P(not nursing major)
From the table, we have:
P(female) = 2428/3538 ≈ 0.686
P(not nursing major) = 1728/3538 ≈ 0.489
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 ≈ 1.175
This probability is greater than 1, which is not possible. Therefore, we need to subtract the probability of being both female and a nursing major (which was counted twice):
P(being female or not being a nursing major) = P(female) + P(not nursing major) - P(female and nursing major)
From the table, we have:
P(female and nursing major) = 700/3538 ≈ 0.198
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 - 0.198 ≈ 0.977
Rounded to the nearest thousandth as needed, the probability of being female or not a nursing major is approximately 0.977.
(c) The probability of not being female or a nursing major is the complement of the probability of being female or a nursing major:
P(not being female or being a nursing major) = 1 - P(being female or being nursing major)
From part (a), we have:
P(being male or being nursing major) ≈ 0.574
Therefore:
P(not being female or being a nursing major) ≈ 1 - 0.574 ≈ 0.426
Rounded to the nearest thousandth as needed, the probability of not being female or a nursing major is approximately 0.426.
(d) The events "being male" and "being a nursing major" are not mutually exclusive, because there are 94 males majoring in nursing (as shown in the table). Mutually exclusive events cannot occur at the same time, but being male and a nursing major is a possible combination. Therefore, the correct answer is OB. Yes, because there are 94 males majoring in nursing.
Explanation: