Let A and B be events with P(A) 6= 0 and P(B) 6= 0. If P(A|B) > P(A), prove that P(B|A) > P(B)

The term is mutually exclusive to be mixed with the term independent. The term mutually exclusive is then related to the occurrence of another event. if two events A and B are independent, P (A) is the prior probability, P (A|B) is the conditional probability of A given B. P( B|A ) is the conditional probability of B given A. it is also called the likelihood of the event.

Question No: 2

Suppose that we throw two unbiased dice independently. Let 

Question 3

The conditions of the question show that a jar contains w white balls, b black balls and r red balls. In order to find the probability of a white ball being drawn before a black ball if each ball is replaced after being drawn following system of equation will be used,

Question No: 4

Let X be a random variable with probability mass function  for x = 1, 2, 3, . . .. by using only the definition of the expected value we can evaluate the expected value of X. Consider that X is a binomial random variable with different parameters n and p. X represent the number of successive trials and it can be written as Consider two situations, when  it shows that the trial is a success while on the other hand if  then trail is a failure. Inserting the values of x =  1,  2,  3, . . .  .  . in the equation gives,