Probability Q

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punitkaur
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Topic: Probability Q

Fri Oct 30, 2009 2:07 pm

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25. 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

mridul_dave
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Sun Nov 15, 2009 11:14 am

punitkaur wrote: 25. 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 The number looke like this _ _ _ _ 1 1 1 in dashes you can have : 2,3,4,5,6,7,8,9 ( 8 possiblities) Possible prime numbers are : 2, 3,5,7 ( 4 possibilities) Probability of a number being a prime in one position = 1/2 First lets count no prime number 1/2 * 1/2 * 1/2 * 1/2 = 1/16 Now lets count prpbability of 1 and only 1 prime number in any of the 4 positions 4 * ( 1/2 * 1/2 * 1/2 * 1/2 ) = 4/16 So probability of prime number in one or no positions = 1/16 + 4/16 = 5/16 Probability of having atleast two numbers prime is 1-5/16 = 11/16 Choose C