Question

Consider an experiment, the events , , , and , and the probabilities p()=0.57, p()=0.48, p(∩)=0.31.

Answer 1

To find the probabilities related to the given experiment, we can use the provided information: a) the probability that the student belongs to a club is 0.90; b) the probability that the student works part time is 0.21; c) the probability that the student belongs to a club AND works part time is 0.03; d) the probability that the student belongs to a club given that the student works part time is 0.1429; e) the probability that the student belongs to a club OR works part time is 0.93.

Step-by-step explanation:

To find the probabilities related to the given experiment, we can use the provided information:

1. a. The probability that the student belongs to a club can be found by adding the probabilities of events C and PT, which gives us 0.40 + 0.50 = 0.90.
2. b. The probability that the student works part time is given as 0.18 + 0.03 = 0.21.
3. c. The probability that the student belongs to a club AND works part time is given as 0.03.
4. d. The probability that the student belongs to a club given that the student works part time can be found by dividing the probability of both events happening (0.03) by the probability of the student working part time (0.21), which gives us 0.03 / 0.21 = 0.1429 (rounded to four decimal places).
5. e. The probability that the student belongs to a club OR works part time can be found by adding the probabilities of events C, PT, and the overlapping section (C ∩ PT), which gives us 0.40 + 0.50 + 0.03 = 0.93.