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password

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password

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5. A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
A 1/32
B 1/16
C 1/8
D 2/5
E ½

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The answer is A


prob. = fav. no. of cases / total no. of cases.

fav. no. of cases = 5*5*5*5*5

total no. of cases = 10*10*10*10*10

hence prob. = 5*5*5*5*5/10*10*10*10*10 = 1/32

logic is...

for favorable no. of cases.

we have to make a password from 5 digits (0,2,3,5,7) means five digits are there to fill five spots.. repetition is allowed as password can be 00000 or 22233.. so first place in five digit password can be filled with 5 options.. similarly for second.. third and so on..

apply this logic for total no. of cases.

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Quote:
5. A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
A 1/32
B 1/16
C 1/8
D 2/5
E ½
The digits: 0,2,3,5,7 fulfill the requirements of the password. The digits 1,4,6,8,9 do not.

Therefore, for the first digit of the password there is a 5/10 = 1/2 chance that it will fit the requirements.

Since repetition is allowed, the same is true for the remaining four digits of the password.

Hence:

(1/2)^5=1/32

The answer is A.

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