4. A total of 2n people, consisting of n married couples, are randomly divided into n pairs. Arbitrarily number the women, and let W,denote the event that woman i is paired with her husband. (a) Find Pr(W;). (b) For i + j, find Pr(W|W;). (c) When n is large, approximate the probability that exactly one wife is paired with her husband. (d) If each pairing must consist of a man and a woman, what does the problem reduce to?

Q: Suppose that A, B are two independent events, with P(A) = 0.3 and P(B) = 0.4. Find P(A and B)

A:

Q: Let X be the number of times '4' is rolled out of a total of 8 rolls.  What is the probability that…

A:

Q: Suppose that A and B are independent events such that P(B) = 0.70 and P (B)=0.20. Find P(An B) and P…

A: Given thatA and B are independent events.such that

Q: assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?

A: Since A and B are independent event, so pr(A∩B)= pr(A)pr(B).

Q: Suppose A = = the event that you get 8 hours of sleep, and B = the event that you exercis If P(A) =…

A: We have given that  P(A) = 0.26 P(B) = 0.37 P(AB) = P( A and B ) = 0.11   Conditional probability…

Q: Let X be the number of students who show up for a professor's office hour on a particular day.…

A: Probability of an event is computed by taking the ratio of number of favourable outcomes to total…

Q: Suppose that A and B are events such that P(A) = 2/7 and P(A&B) = 3/25. Determine P(B| A).

A:

Q: Suppose that A and B are independent events such that P (4)=0.40 and P(B)-0.70. Find P(ANB) and P…

A: We have given that A and B are independent events.

Q: P(lightning | rain) = P(rain | lightning):

A: We have given that  The total number of days = 365 Rainy days = 103 Lightning days = 20 Rainy and…

Q: Suppose that A, B are two independent events, with P(A) = .1 and P(B) = .2. Find P(A|B).

A:

Q: Part (a) Construct a tree diagram of the situation.   Part (b) P(C) =   Part (c) P(F | C) =

A: Given ,      C - A man develop s cancer     P(c) = 0.4956    F = A man has atleast one false…

Q: Suppose that A and B are independent events such that P (A) = 0.10 and P(B) = 0.50. Find P(An B) and…

A: P(A)=0.1P(B)=0.5events A and B are independent

Q: Three students X, Y and Z, each shoot at a target. The probability of hitting the 1 5 target by X, Y…

A:

Q: A family has 5 children, either boy or girl. The probability of each outcome is equal. Let A="the…

A: Given A="the first child is a girl"We can have first child to be girl in 1 way only.For each other…

Q: he probability that a patient recovers from a disease is 0.8. Suppose 5 people are known to have…

A: Given data, p=0.8 n=5

Q: The E be the event that a new car requires engine work under warranty and let T be the event that…

A: Probability: If random experiment results in n mutually exclusive and equally likely outcomes; out…

Q: Suppose a basketball player who makes a free throw shot with success 80%. Let X be the number of…

A: From the provided information,Probability of success (p) = 0.80n = 5

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.