Question

1-in-6 wins Alan decides to use a different strategy for the 1-in-6 wins game of Exercise 85. He keeps buying one 20-ounce bottle of the soda at a time until he gets a winner. (a) Find the probability that he buys exactly 5 bottles. Show your work. (b) Find the probability that he buys no more than 8 bottles. Show your work.

Answer 1

Answer:

a) $P(X=5) = 0.06691$

b) $P(X \leq 8) = 0.791784$

Explanation:

Given data:

Probability of success = 1/6

1) Probability of buying 5  same bottles is calculated as

from information given we have

percentile x = 5

Probability of success = 1/6

hence from geometric distribution calculator we have

geometpdf (1/6, 5) = 0.06691

$P(X=5) = 0.06691$

2) probability of buying not more than 8 bottles

percentile x = 8

geometpdf(1/6, 8) = 0.791784

$P(X \leq 8) = 0.791784$

Answer 2

a). The probability of buying exactly 5 bottles would be:

$P(X = 5) = 0.06691$

b). The probability of buying bottles not more than 8 would be:

$P(X$ ≤ $8) = 0.791784$

a). Given that,

The winning probability = 1/6

To find,

The probability of buying exactly 5 bottles with percentile $(X = 5)$ employing geometric distribution calculator $1 - P^{x-1} p$

$= (1/6, 5)$

$= 0.06691$

b). The probability of buying bottles not more than 8

$= (1/6, 8)$

$P(X$ ≤ $8) = 0.791784$  

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