Events $A$ and $B$ are independent. Suppose event $A$ occurs with probability 0.86 and event $B$ occurs with probability 0.70 .
Compute the following.
(If necessary, consult a list of formulas.)
(a) Compute the probability that $A$ occurs but $B$ does not occur.
(b) Compute the probability that $A$ occurs or $B$ does not occur (or both).
Answer
Final Answer: (a) The probability that A occurs but B does not occur is \(\boxed{0.258}\). (b) The probability that A occurs or B does not occur (or both) is \(\boxed{0.902}\).
Step 1 ：Given that events A and B are independent, with the probability of event A occurring being 0.86 and the probability of event B occurring being 0.70.
Step 2 ：For part (a), we need to find the probability that event A occurs but event B does not. Since A and B are independent, the probability of A occurring and B not occurring is the product of the probability of A and the probability of not B. The probability of not B is 1 - 0.70 = 0.30. Therefore, the probability of A occurring and B not occurring is 0.86 * 0.30 = 0.258.
Step 3 ：For part (b), we need to find the probability that either A occurs or B does not occur (or both). This can be found using the formula for the probability of the union of two events: P(A U not B) = P(A) + P(not B) - P(A ∩ not B). Therefore, the probability of A occurring or B not occurring (or both) is 0.86 + 0.30 - 0.258 = 0.902.
Step 4 ：Final Answer: (a) The probability that A occurs but B does not occur is \(\boxed{0.258}\). (b) The probability that A occurs or B does not occur (or both) is \(\boxed{0.902}\).
