Question

1. Show your work for the following

- If P(A) = 0.7, P(B) = 0.1 and A and B are mutually exclusive, find P (A or B).

- If P(A) = 0.5, P(B) = 0.4, and P(A or B) = 0.8, are A and B mutually exclusive?

- If P(B) = 0.6, find P(B^c).

2. Determine whether events A and B are mutually exclusive.

A: Jayden has a math class on Tuesdays at 2:00. B: Jayden has an English class on Tuesdays at 2:00.

3. In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of

the women received an A in the course. A student is chosen at random from the class.

a. Find the probability that the student is a woman.

b. Find the probability that the student received an A.

c. Find the probability that the student is a woman or received an A.

d. Find the probability that the student did not receive an A.

Answer #1

1.a) If A and B are mutually exclusive, P(A or B) = P(A) + P(B)

= 0.7 + 0.1

= **0.8**

b) P(A) + P(B) = 0.5 + 0.4 = 0.9

P(A or B) = 0.8

P(A or B) P(A) + P(B)

So, A and B are **not mutually exclusive**

c) P(B^{c}) = 1 - P(B)

= 1 - 0.6

= **0.4**

2. Both events cannot occur at the same time. So, **the
events are mutually exclusive**.

3. a) P(woman) = **17/30**

b) P(received an A) = 5/30

= **1/6**

c) P(woman or received an A) = (17 + 5 - 3)/30

= **19/30**

d) P(student did not receive an A) = (30-5)/30

= **5/6**

Let A and B be events with P(A) = 0.7, P(B) = 0.9, and P
(A and B) = 0.6.
Compute P (A or B)
Are A and B mutually exclusive? Explain.

Let A and B be two events such that P(A) = 0.8, P(B) = 0.6 and
P(A B) = 0.4. Which statement is correct?
a.
None of these statements are correct.
b.
Events A and B are independent.
c.
Events A and B are mutually exclusive (disjoint).
d.
Events A and B are both mutually exclusive and independent.
e.
Events A and B are the entire sample space.

Consider the following scenario:
• Let P(C) = 0.7
• Let P(D) = 0.4
• Let P(C|D) = 0.8
Q1. P(C AND D) =
Q2. Are C and D Mutually Exclusive?
Q3 Are C and D independent events?
Q4. P(D|C) =
Round your answer to two decimal places.

Given P(A) = 0.7 and P(B) = 0.4 1) If A and B are independent
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