Question

P(A|B) = 1/3

P(A|B^c) = 2/3

P(B|A) = 1/2

What is...

P(A)

P(B)

P(B^c|A^c)

^c means complement

Answer #1

Suppose events A, B, and C are MUTUALLY INDEPENDENT and P(a) =
1/4, P(B) = 1/3, and P(C) =1/2 and N denotes the total number of
events among A, B, C, that occur
(a) Draw a venn diagram
(b) What is the E(N)
(c) What is E(N^2)
(d) What is Cov(Ia,N)
(e) Find P(N <= 2 | C)
Thank you!

7. Events A and B are independent. The P(A) = 3/5, P(not B) =
2/3. What is P(A and B)? a. 2/5 b. 1/5 c. 4/15 d. 2/15
8. A bag contains 4 red marbles, 3 blue marbles, and 7 green
marbles. If a marble is randomly selected from the bag, what is the
probability that it is blue? A) 1/11 B) 3/14 C) 1/7 D) 1/3
9. The distribution of the heights of students in a large class
is...

Given the following information on Events A, B, C, and D.
P(A) = 0.35
P(A U D) = 0.55
P(A n D) = 0.12
P(B) = 0.18
P(A I B) = 0.43
P(C) = 0.25
P(A n C) = 0.07
1.Compute P(D).
2.Compute P(A n B).
3.Compute P(A I C).
4.Compute the probability of the complement of C
5. Are events A and C independent? Explain.

Show that provided, P(B∩C)>0, [3+3=6]
•P(A|B) = 0 will imply that P(A|B∩C) = 0.
•P(A|B) = 1 will imply thatP(A|B∩C) = 1.

Provide an example of a probability space and three events A, B,
C such that P(A∪B∪C)=P(A)+P(B)+P(C)−1/2.

Suppose that P(A)=1/2 and P(B)=1/3
Assume that A and B are neither independent nor disjoint, but
that it is known that P(A|B)=1/4. Recalculate the probabilities
listed.
a. P(A∩B):
b. P(A∪B):
c. P(A|B):
d.P(B|A):

P(A)=0.35
P(B)=0.65
P(A or B)=0.89
1. P(not A)
2. P(A and B)
3. determine if the events A and B are independent.

Suppose events A, B, C have the following probabilities: P(A|B)
= 1 ／3 , P(C|B) = 23 ／45 , P(A ∩ C|B) = 11 ／45 . Given that B has
occurred, a) Find the probability that only C has
occurred. b) Find the probability that only A or only C
has occurred, but not both. c) Find the probability that
A or C has occurred.

If p is an odd prime and if
1+ 1/2 +1/3 +...+1/p-1=a/b , where a,b are positive integers ,
prove that a is divisible by p.

Suppose that A and B are two events in a sample space
S with P(B)=0.04, P(A n B)=0.03 and P(A u B) =0.46
a) what is P(B) complement
b)what is P(A)
c)what is P( AUB) complement
d)what is P(A/B)
e)what is P(A complement n B)
f)Are two events A and B independent? justify your answer.
g) Are two events A and B mutually exclusive? Justify your
answer.

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