Probability Q

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