Let A and B be two events in a sample with P(A)=0.4 and
P(AuB)=0.7.Let P(B)=p
a)i For what value of p are A and B mutually exclusive?
ii for what value of p are A and B independent?
b) Assume that P(A)=0.4 and P(B)=0.3
i find P(B')
ii if A and B are mutually exclusive , what is P(A or B)
ii given that P(A or B)=0.6, Find the P(B/A)
c) suppose events A and B are such that P(A)=0.25,P(B)...
Let P ( A ) = 0.5, P ( A ∩ B ) = 0.2 and P ( A | B ) = 0.5.
Determine P ( B ) = (as a decimal) and P ( A ∪ B )
= (as a decimal)
Three identical light bulbs are connect in parallel. If the
probability of the system to operate normally is 99.2%, determine
the probability of each light bulb to fail p = (as a
decimal).
6. If ?(?) = 0.5 and ?(?|?) = 0.4, are events ? and ?
independent? Why or why not?
7. A report on addiction notes that 16% of Americans have the
disease of addiction, and 90% of them receive no form of treatment.
Determine the probability that a randomly selected American has the
disease of addiction and receives no form of treatment.
(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then
a∣c.
(B) Let p ≥ 2. Prove that if 2p−1 is prime, then p
must also be prime.
(Abstract Algebra)
Q. Let A, B independent events, with P(A) = 1/2 and P(B) = 2/3.
Now C be an event with P(C) = 1/4, and suppose that P(A|C) = 1/3,
P(B|?̅) =7/9, P(A∩B|?̅) = 7/18.
(a) Calculate the P(A∩B)
(b) Calculate the P(A|?̅) and P(B|C)
(c) Calculate the P(A∩B|C)
(d) Show if P(A∩B|C) equals P(A|C)P(B|C) or not.
Let A and B be two events in a sample space S. If P(A1Bc) =.10,
P(Ac1B) =.40 and P(Ac1Bc) =.10,
a. Illustrate the events A1Bc, Ac1B and Ac1Bc on a van
Venn-diagram
b. Check for the independence of events A and B.
c. Find P(A1B*AUB).
67. Suppose that P(B) = 0.4, P(A|B) = 0.1 and P(A|B^c) =
0.9
(a) Calculate P(A)
(b) Calculate P(A|B)
71. Suppose a couple decides to have three children.
Assume that the sex of each child is independent, and the
probability of a girl is 0.48, the approximate figure in the
US.
(a) How many basic outcomes are there for this
experiment? Are they equally likely?
(b) What is the probability that the couple has at least
one girl?
104. A...