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Re: A password for a computer uses five digits from 0 to 9, inclusive. Wha [#permalink]
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Bunuel wrote:
A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


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Prime numbers from 0 to 9: 2,3,5,7 (4 in number) and 0 = 5 favourable cases.

Total cases (0-9 digits) = 10

Probability of one digit to be Prime or Zero = (5/10) = 1/2

(1/2) will be the probability of one of the 5 digits of password to be Prime or Zero. But since password uses 5 digits so the probability of every place needs to be taken

Probability of all 5 digits to be prime or zero = (1/2)*(1/2)*(1/2)*(1/2)*(1/2) = (1/2)^5 = 1/32
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Re: A password for a computer uses five digits from 0 to 9, inclusive. Wha [#permalink]
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Allowed digits - (0, 2, 3, 5, 7).

Sample space = 10*10*10*10*10 = 10^5.

Favourable event - 5*5*5*5*5 = 5^5.

Probability = 5^5/10^5 = (5/10)^5 = (1/2)^5 = 1/32. Ans (A).
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Re: A password for a computer uses five digits from 0 to 9, inclusive. Wha [#permalink]
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Bunuel wrote:
A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


Kudos for a correct solution.


We have combinations with repetition and order does matter here.

Possible Combinations = Primes and 0's / Total combinations = 5^5/10^5 = 1/32

Answer A
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Re: A password for a computer uses five digits from 0 to 9, inclusive. Wha [#permalink]
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Bunuel wrote:
A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


Kudos for a correct solution.


Numbers can repeat. Therefore, there are 10^5 possible choices.

If only prime numbers and zeros can be picked, that's 0, 2, 3, 5, and 7 - 5 total numbers. All of these can repeat as well. There are 5^5 possible choices.

5^5/10^5 = 5^5/(2^5*5^5) = 1/2^5 = 1/32

A
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Re: A password for a computer uses five digits from 0 to 9, inclusive. Wha [#permalink]
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Bunuel wrote:
A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


Kudos for a correct solution.


800score Official Solution:

To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 × 10 × 10 = 100,000 possible combinations.

Prime numbers constitute 2, 3, 5 and 7. In addition to zero, this is 5 total possibility for each digit. So the number of satisfactory variants is 5 × 5 × 5 × 5 × 5. So the probability is 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32.

The right answer is choice (A).
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Re: A password for a computer uses five digits from 0 to 9, inclusive. Wha [#permalink]
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Bunuel wrote:
A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


Kudos for a correct solution.


Total possible passwords = 10*10*10*10*10

Single digit prime numbers are {2, 3, 5, 7} I.e. 4 prime numbers
So we have 4 choices {2,3,5,7} for each digit

i.e. Favorable outcomes = 5*5*5*5*5

Probability = (5*5*5*5*5) / (10*10*10*10*10) = 1/32

Answer option A
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Re: A password for a computer uses five digits from 0 to 9, inclusive. Wha [#permalink]
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Expert Reply
Bunuel wrote:
A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


We need to determine the probability that a 5-digit code, formed from numbers 0 to 9 inclusive, consists of only prime numbers or 0.

There are a total of 5 digits that are 0 or prime (recall that 1 is NOT a prime number):

0, 2, 3, 5, 7

The probability of selecting one of these digits is 5/10 = 1/2.

Thus, the probability that a password will consist solely of prime numbers or zero is:

1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32.

Answer: A

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