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
George C.
Feb 12, 2016

#0.95^10 ~~ 0.6#

Explanation:

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

#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#

#= ((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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