The probability that Jacqueline will be elected to the student council is 0.6, and the probability that she will be selected to represent her school in a public speaking contest is 0.75. The probability of Jacqueline achieving both of these goals is 0.5.
A) are these two goals, mutually exclusive, explain your answer
B) are these two girls independent explain your answer
C) what is the probability that Jacqueline is either elected to the student council, or picked for the public speaking contest
A) No, these two goals are not mutually exclusive. This is because the probability of Jacqueline achieving both goals is 0.5, which means there is an overlap in the outcomes of being elected to the student council and being selected for the public speaking contest.
B) To determine if these two events are independent, we need to compare the probability of one event happening given that the other event has occurred. In this case, the probability of Jacqueline being elected to the student council is 0.6 and the probability of her being selected for the public speaking contest is 0.75.
To assess independence, we need to compare these probabilities with the probability of both events occurring together. The fact that the probability of both events occurring (0.5) is different from the product of the individual probabilities (0.6 * 0.75 = 0.45) suggests that these events are dependent on each other. Therefore, the two events are not independent.
C) To calculate the probability that Jacqueline is either elected to the student council or selected for the public speaking contest, we need to find the union of these two events. Since the events are not mutually exclusive, we can use the formula P(A or B) = P(A) + P(B) - P(A and B).
P(A) = 0.6 (probability of Jacqueline being elected to the student council)
P(B) = 0.75 (probability of Jacqueline being selected for the public speaking contest)
P(A and B) = 0.5 (probability of both events occurring together)
P(A or B) = 0.6 + 0.75 - 0.5 = 0.85
Therefore, the probability that Jacqueline is either elected to the student council or selected for the public speaking contest is 0.85.
A) No, these two goals are not mutually exclusive. This is because the probability of Jacqueline achieving both goals is not zero (0.5), indicating that it is possible for her to be both elected to the student council and selected for the public speaking contest. If the events were mutually exclusive, then the probability of both events occurring would be zero.
B) These two events, being elected to the student council and being selected for the public speaking contest, may not be independent based on the given information. In order for two events to be independent, the probability of one event occurring should not be affected by the occurrence or non-occurrence of the other event. However, since the probability of Jacqueline achieving both goals (0.5) is different from the product of the individual probabilities (0.6 x 0.75 = 0.45), it suggests that these events are dependent.
C) To determine the probability that Jacqueline is either elected to the student council or picked for the public speaking contest, we can use the addition rule of probability. The addition rule states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.
P(elected or picked) = P(elected) + P(picked) - P(elected and picked)
Given that P(elected) = 0.6, P(picked) = 0.75, and P(elected and picked) = 0.5, we can calculate:
P(elected or picked) = 0.6 + 0.75 - 0.5
= 0.85
Therefore, the probability that Jacqueline is either elected to the student council or picked for the public speaking contest is 0.85.