A telephone company claims that directory assistance will give you the right number 95% of the time you make calls. If you make 10 calls, what would be the probability of getting the right number all 10 times?

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A telephone company claims that directory assistance will give you the right number 95% of the time you make calls. If you make 10 calls, what would be the probability of getting the right number all 10 times?

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Answer 1 · 2016-02-12T21:10:42

${0.95}^{10} \approx 0.6$ $0.95^10 ~~ 0.6$

Explanation:

Assuming that the probability associated with each of the $10$ $10$ calls is independent, the probability of all $10$ $10$ numbers being right is:

${0.95}^{10} = 0.59873693923837890625 \approx 0.6$ $0.95^10 = 0.59873693923837890625 ~~ 0.6$

Rather than calculate this exactly, you can use the binomial theorem to give an approximation:

${0.95}^{10} = {(1 - 0.05)}^{10}$ $0.95^10 = (1 - 0.05)^10$

$= ((10),(0))1 - ((10),(1))0.05 + ((10),(2))0.05^2 -...$

$~~1 - 10*0.05 + 45*0.0025$

$= 1 - 0.5 + 0.1125 = 0.6125 ~~ 0.6$

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A telephone company claims that directory assistance will give you the right number 95% of the time you make calls. If you make 10 calls, what would be the probability of getting the right number all 10 times?

1 Answer

Explanation:

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