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Probabilty question Phone number

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by abhi.genx7 » Thu Oct 21, 2010 3:29 am
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) 1/2
e) 5/8
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by abhi.genx7 » Thu Oct 21, 2010 3:31 am
OA is B.
I could not figure out how to approach the problem.
A step by step approach would be helpful
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by frank1 » Thu Oct 21, 2010 8:10 am
Ok
the final answer can be setup like this
[1- ((1/2)^4+(1/2)^4*4)] = 11/16

But i would recommend doing this question this way

we have 7 variables of which 3 are already reserved so we can work with only 4 slots
we have 4 prime digits (2, 3, 5, 7) and 4 non-prime digits (4, 6, 8, 9), the probability of choosing a prime digit is 1/2 and non prime is also 1/2
we need at least 2 Primes
which means
1-(no primes+1 prime)
so we represent non prime as NP and Prime as P
We have no prime
NP NP NP NP =1/2X1/2X1/2X1/2=1/16
and 1 prime cases
NP NP NP P=1/16
NP NP P NP=1/16
NP P NP NP=1/16
P NP NP NP=1/16

So we have 1/16+4/16=5/16

so 1-5/16=11/16
so it is B

Thanks
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