Question

Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected​ (with replacement). Find the probability that for one such phone​ number, the last four digits include at least one 0.'

Answer 1

probability at least one zero is 0.3439

Explanation:

given data

last four digits = randomly selected​

to find out

probability that for one such phone​ number the last four digits include at least one 0.

solution

we know there are total 10 digit

so we first find probability of non zero digit i.e.

Probability ( non zero ) = 9 /10 = 0.9

and now we find probability of none of digit zero only event happen n= 4 time in a row by multiplication rules i.e

Probability ( none zero in 4 digit ) =
`0.9^(n)`

Probability ( none zero in 4 digit ) =
`0.9^(4)`

Probability ( none zero in 4 digit ) = 0.6561

so we can say probability at least one zero = 1 - Probability ( none zero in 4 digit )

probability at least one zero = 1 - 0.6561

probability at least one zero is 0.3439