Question

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?

Answer 1

`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`