The probability that a randomly selected box of a certain type of cereal has a p

Question

The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.1. Suppose you purchase box after box until you have obtained four of these prizes (a) What is the probability that you purchase x boxes that do not have the desired prize? O nb(x: 4, 1, 10) O nb(x; 4, 0.1) b(x; 4, 1, 10) O b(x 4, 0.1) O h(x; 4, 1, 10) (b) What is the probability that you purchase six boxes? (Round your answer to four decimal places.) 0.0045 e) What is the probability that you purchase at most six boxes? (Round your answer to four decimal places.) 0.0114 (d) How many boxes without the desired prize do you expect to purchase? 36 How many boxes do you expect to purchase? 36

Explanation / Answer

b) probability that you purchase 6 boxes =P( till 5 box you got 3 prizes and in 6th you got 4th one)

=(5C3)(0.1)4(0.9)2 =0.0008

c)probability of purcahsing at most 6 boxes =1-P( at most 3 prize till 6 box) =1-x-03 (6Cx)(0.1)x(0.9)6-x

=0.0013

d) expected box to purchase without desired priize =r/p -r =4/0.1 -4 =36

number of boxes to be purchased =r/p=40

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