Probability... pls explain?

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 353
Joined: Sat Jan 20, 2007 1:29 am
Location: Italy
Thanked: 7 times
GMAT Score:720

Probability... pls explain?

by mjjking » Fri Feb 27, 2009 6:50 am
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 nowhere else and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?

15/16
11/16
11/12
½
5/8

OA is B
Beat The GMAT - 1st priority
Enter a top MBA program - 2nd priority
Loving my wife: MOST IMPORTANT OF ALL!

REAL THING 1 (AUG 2007): 680 (Q43, V40)
REAL THING 2 (APR 2009): 720 (Q47, V41)
Source: — Problem Solving |

Master | Next Rank: 500 Posts
Posts: 221
Joined: Wed Jan 21, 2009 10:33 am
Thanked: 12 times
Followed by:1 members

by krisraam » Fri Feb 27, 2009 8:02 am
The last 3 digits are 1 and none of the digits is 0

Number is in this form -- -- -- -- 1 1 1.

we will find the probablity of having no prime digit and one prime digit

The set of numbers to choose { 2,3,4,5,6,7,8,9}

Total no. of possible numbers = 8^4 ( Each position of the number can be one of the possible 8 numbers.

Probablity of having no prime digit.

The set of numbers to choose {4,6,8,9}

Total no of numbers formed = 4^4


Probablity of having one prime digit.

The set of numbers to choose {2,3,5,7}

we have to select one from this set and 3 from non prime set

You can select one number from 4 in 4C1 ways = 4

The number being selected can take any of the four places availabe

The reamining 3 places can be filled in 4^3 ways

Total numbers formed that way = 4*4*4^3 = 4*4^4

1- ( 4^4 + 4*4^4)/8^4

= 11/16

Thanks
raama