Consider the population of voters described in example 3.6. suppose that there are n = 5000 voters in the population,40% of whom favor jones. identify the event favors jones as a success 8. it is evident that the probability of s on trial 1 is.40. consider the event b that 8 occurs on the second trial then b can occur two ways: the first two trials are bothsuccesses or the first trial is a failure and the second is a success. show that p( b) = .4. what is p( b| the first trial is 5)? doesthis conditional probability differ markedly from p( b)? referencesuppose that 40% of a large population of registered voters favor candidate jones. a random sample of n = 10 voters willbe selected, and y, the number favoring jones, is to be observed. does this experiment meet the requirements of abinomial experiment? if each of the ten people is selected at random from the population, then we have ten nearly identical trials, with each trialresuiting in a person either favoring jones (8) or not favoring jones (f). the random variable of interest is then the numberof successes in the ten trials. for the first person selected, the probability of favoring jones (8) is .4. but what can be saidabout the unconditional probability that the second person will favor jones? in exercise 3.35 you will show thatunconditionally the probability that the second person favors jones is also .4. thus, the probability of a success 5 stays thesame from trial to trial- however, the conditional probability of a success on later trials depends on the number ofsuccesses in the previous trials. if the population of voters is large, removal of one person will not substantially change thefraction of voters favoring jones, and the conditional probability that the second person favors jones will be very close to.4. in general, ifthe population is large and the sample size is relatively small, the conditional probability of success on alater trial given the number of successes on the previous trials will stay approximately the same regardless of the outcomeson previous trials. thus, the trials will be approximately independent and so sampling problems of this type areapproximately binomial