perplexus.info :: Probability : 7 come zero

7 come zero (Posted on 2018-06-28)

Let N be a randomly chosen 5-digit number.

a. What is the probability that N contains at least one zero?
b. What is the probability that N contains at least one 7?
c. What is the probability that it contains exactly one zero and one 7?

d. Generalize the above questions for a n-digit number , n>1.

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Part C (spoiler)

| Comment 2 of 5 |

Assuming leading zeroes, the 0 can be in 5 places, after which the 7 can be in 4 places, after which the remaining 3 places can each have one of 8 different digits.

Total numbers = 5*4*8*8*8 = 10240.

Probability = 10240/100000 = .1024

If there are n digits, probability = n*(n-1)*8^(n-2)/10^n

Posted by Steve Herman on 2018-06-28 09:38:03

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