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.'

Question

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-08-01T10:24:29+02:00

Answer:

probability at least one zero is 0.3439

Step-by-step 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 ) = [tex]0.9^{n}[/tex]

Probability ( none zero in 4 digit ) = [tex]0.9^{4}[/tex]

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