Question

#18

Events A and B are mutually exclusive. Suppose event occurs with probability 0.05 and event occurs with probability 0.36. a. Compute the probability that B occurs or does not occur (or both). b. Compute the probability that either occurs without occurring or occurs without occurring. (If necessary, consult a list of formulas.) ?

#19

Events and are mutually exclusive . Suppose event occurs with probability 0.11 and event B occurs with probability 0.81. If does not occur, what is the probability that occurs? Round your answer to at least two decimal places . (If necessary , consult a list of formulas .)

#20

Events A and are independent. Suppose event A occurs with probability 0.12 and event B occurs with probability 0.27. a. If event A or event occurs, what is the probability that B occurs? b. If does not occur, what is the probability that occurs? Round your answers to at least two decimal places. (If necessary, consult a lis of formulas.)

#21

Events A and B are independent . Suppose event A occurs with probability 0.69 and event occurs with probability 0.75. a . Compute the probability that A occurs but does not occur . b. Compute the probability that either occurs without occurring or and B both occur. ( If necessary , consult a list of formulas .) ?

Events A and are mutually exclusive. Suppose event A occurs with probability 0.05 and event B occurs with probability 0.36.

a. Compute the probability that occurs or A does not occur (or both).

b. Compute the probability that either A occurs without Boccurring or occurs without occurring. (If necessary, consult a list of formulas.) ?

this is hope the question is asked

Answer 1

The formulas or concept that will be repeatedly used in this problem are

Probability of joint occurence is always zero, i.e.

Probability of joint occurence is the product of individual probabilities, i.e.

Hence, we can deal with them now

a. P(B occurs or A does not occur or both) = P(B occurs)  

(because if B occurs, then it is evident that A will definitely not occur, so it is not a different condition)

= 0.36

b. P(A occurs without B occurring or B occurs without A occurring) = P(A) + P(B)

(again by definition of mutually eclusive, if one occurs then it is definite that other does not occur)

= 0.05 + 0.36 = 0.41

Event names are not mentioned in the question statement.

"If does not occur, what is the probability that occurs" could mean two different things.

It it actually means "If A does not occur, what is the probability that B occurs" then the answer is 0.81

It it actually means "If B does not occur, what is the probability that A occurs" then the answer is 0.11

If event A or event B occurs, what is the probability that B occurs?

First, we find the probability that either A or B occurs (the union)

Now we apply the conditional probability

"If does not occur, what is the probability that occurs" could again mean two things

If it means "If A does not occur, what is the probability that B occurs" then the answer is

If it means "If B does not occur, what is the probability that A occurs" then the answer is

P(A occurs but B does not occur) = P(A) * P(not B) = 0.69 * (1 - 0.75) = 0.1725

Second stateent is again ambiguous