Give reasons for your I. Decide if each of the following situations fits the bin
ID: 2926814 • Letter: G
Question
Give reasons for your I. Decide if each of the following situations fits the binomial setting. answer in each case. If x has a binomial distribution, state the values of n and p. a. Roll a fair die until it b. Roughly 60% of Americans believe that extraterrestrial life exists on other planets. A random sample of 10 Americans is selected and during phone interviews are asked their opinion on extraterrestrial life. Let x be the number who say they believe in extraterrestrial life. c. A deck of cards is shuffled. You draw a card and check to see if it is a red card and then put it aside. Then you draw a second card and check to see if it is a red card and put it on top of the first card drawn. You continue until you have drawn 5 cards. Let x be the number of red cards in the five that were drawn.Explanation / Answer
a. Here, the event is of getting the first six on the nth roll. This is maximum at the first roll and keeps on decreasing as the number of rolls increase.
On the first roll, probability is 1/6.
On the second roll, probability is 5/6*1/6.
On the nth roll, probability is (5/6)^(n-1)*1/6.
As this is decreasing on every roll, it is not a binomial setting.
b. Here, ten distinct people are selected. So, there is no replacement of people. This means that this is not a binomial setting.
In practice, the population of America is much greater than than the sample size. So, we can say that for all practical purposes, this is almost a binomial distribution. There is anyway a very low probability of choosing the same person twice even if replacement is done. In that case, we can assume this to be a binomial setting. Then, n will be the population of America and p will be 0.6.
c. Here, a card is removed from the deck and kept aside. Hence, it is not being replaced back in the deck. So probability of second card being red depends on probability of first card being red. So, the binomial setting does not apply here.
Binomial setting only applies when events are independent, i.e. probability of second event is not affected by probability of first event.
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