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 0.2. Suppos (a) What is the probablity that you purchase x boxes that do not have the desired prize? O nb(x; 2, 2, 10) O h(x: 2, 0.2) O h(x; 2, 2, 10) O b(x; 2, 0.2) O b(x: 2, 2, 10) (b) What is the probability that you purchase four boxes? (Round your answer to four decimal places.) (e) What is the probability that you purchase at most four boxes? (Round your answer to four decimal places 0559] (d) How many boxes without the desired prize do you expect to purchase? How many boxes do you expect to purchase?

Explanation / Answer

Solution:

We know that p = 0.2 and q = 1 - p = 1 - 0.2 = 0.8

b. P (X = 4) = (0.8)^4-1 (0.2)

P (X = 4) = 0.1024

c.

P (X 4) = 1 – q^k

                =1 – (0.8)^4

                = 0.5904

d. Expected number without the desired prize you expect to purchase = q/p = 0.8/0.2 = 4

Expected number you expect to purchase = 1/p = 1/0.2 = 5

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