An urn contains n+m balls, of which n are red and m are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. Find E[X]. To obtain this quantity, number the red balls from 1 to n. Now define the random variables Xi , i=1,....,n by

Xi = 1 if red ball I is taken before any black ball is chosen

0 otherwise

a) Express X in terms of the Xi
b) Find E[X]

Problem 2

From the above problem, let Y = number of red balls chosen after the first but the second black ball has been chosen

a) express Y as the sum of n random variables, each of which is equal to either 0 or 1

... Given that you are awarded at least one contract, fid the conditional probability that (in ... The sum of the probabilities of these three simple events is 0.78 ...

... The expert determines how to calculate conditional probabilities. Calculates of the binomial probability for k successes are provided. Posting ID: 276464:

... b)using the table calculate the conditional probability of C given each of the age groups, or p(c/d), P(c/e), etc compare these probabilities and speculate as ...

... (d)This is conditional probability question: P(woman has disease with man has disease)=P(the married couple)/P(75-79man, 4.9%)=0.0027/4.9%=5.51%. ...

... is female = probability(customer female & under 18)/probability(under 18 ... describes how to derive absolute, joint, relationship, conditional probabilities from a ...

... This can be solved by using the formula for conditional probabilities. The conditional probability of one event given that another event has occurred is equal ...