John wrote a phone number on a note that was later lost.

Question

John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?

a) 15/16
b) 11/16
c) 11/12
d) ½
e) 5/8

walker · Answer

B

our number: XXXX111 where X is out of {2,3,5,7} (prime numbers) or of {4,6,8,9} (not prime numbers)
The probability of getting a prime number (not a prime number) for X is 1/2

So,  P=1-\frac{1}{2^4}-C^4_1*\frac{1}{2^4}=1-\frac{5}{16}=\frac{11}{16}

Edited to correct some typos

ldpedroso · Answer

Walker, could you explain this formula better?

tks

walker · Answer

P_1=\frac{1}{2^4}  - probability of getting 4 not prime digits

P_2=C^4_1*\frac{1}{2^4}  - probability of getting 3 not prime digits and 1 prime digit.

P=1-P_1-P_2  - probability of getting at least 2 prime digits

ldpedroso · Answer

Walker,

Could you explain better the formula P2? I'm not familiaa with it.

thanks again

prateekpuri · Answer

What is the OA.
Given explanation assumes that 1 does not occur in the first 4 places. However the question only says that 1 occurs in the last 3 places. It does not say anything about 1 not occuring anywhere else.

John wrote a phone number on a note that was later lost.

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