A company’s revenue is considerably below expectation with probability

korporasidn

korporasidn

Answered question

2021-11-15

A company’s revenue is considerably below expectation with probability 0.08, is slightly below expectation with probability 0.19, exactly meets expectation with probability 0.26, is slightly above expectation with probability 0.36, and is considerably above expectation with probability 0.11. Let A be the event that the revenue is not below expectation. Let B be the event that the revenue is not above expectation. FIND the probability of the intersection and union of these two events?

Answer & Explanation

Supoilign1964

Supoilign1964

Beginner2021-11-16Added 19 answers

Step 1
Let O1 denote that a company’s revenue is considerably below expectation.
Then, P(O1)=0.08
Let O2 denote that a company’s revenue is slightly below expectation.
Then, P(O2)=0.19
Let O3 denote that a company’s revenue exactly meets expectation.
Then, P(O3)=0.26
Let O4 denote that a company’s revenue is slightly above expectation.
Then, P(O4)=0.36
Let O5 denote that a company’s revenue is considerably above expectation.
Then, P(O5)=0.11
Let A be the event that the revenue is not below expectation and B be the event that the revenue is not above expectation.
Step 2
A = event that the revenue is not below expectation
Events that denote, the revenue is not below expectation are: O3, O4, O5
Then, 

 P(A)=P(O3)+P(O4)+P(O5)
=0.26+0.36+0.11
=0.73
B= event that the revenue is not above expectation.
Events that denote, the revenue is not above expectation are: O1, O2, O3
Then,
P(B)=P(O1)+P(O2)+P(O3)
=0.08+0.19+0.26
=0.53
(a) Probability of Intersection of events A and B is obtained as follows:
Favorable outcomes of event A are: {O3, O4, O5}
Favorable outcomes of event B are: {O1, O2, O3}
Intersection of A and B is the common term between the two events: i.e., O3
P(A and B)=P(O3)=0.26
Therefore, Probability of Intersection of events A and B is 0.26
Step 3
(b) To find the probability of union of these two events:
Using the formula:
P(AB)=P(A)+P(B)P(AB)
Substitute the probability values of A and B as follows:
P(AB)=P(A)+P(B)P(AB)
=0.73+0.530.26
=1
Therefore, probability of union of these two events is 1

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?