BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Probability

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Sat Mar 10, 2007 4:04 am
Thanked: 1 times
Followed by:1 members

Probability

by f2001290 » Tue May 29, 2007 7:30 am
A Four digit safe code does not contain the digits 1 and 4 at all. What is the probability that it has at least one even digit?

I don't have an OA.

P(atleast one digit is even) = 1 - P(all digit odds)

We have 4 odd digits excluding 1 (3,5,7,9).
So, possible 4 digit odd numbers = 4*4*4*4
All possible 4 digit numbers = 7*8*8*8 (Ensure that 1st digit is not 0 and exclude 1 and 4)

P(all digits odd) = 4*4*4*4/7*8*8*8 = 1/14
P(atleast one digit is even) = 1 - 1/14 = 13/14

Any different solution for this . I am very bad at probability
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Sun Mar 18, 2007 9:35 am
Location: mumbai
Followed by:1 members

by RAGS » Tue May 29, 2007 11:03 am
4 digit safe code without 1 and 4
possible digits for each digit 0,2,3,5,6,7,8,9 ie 8 ways
total 8*8*8*8

consider all odd digits so possible digits 3,5,7,9 ie 4 ways
total 4*4*4*4

So atleast one even is= 8*8*8*8 -4*4*4*4 / 8*8*8*8

= 1 - 1/16 = 15/16

Why should the first digit not be zero????????????
If It Is To Be It Is Up To Me
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Sat Mar 10, 2007 4:04 am
Thanked: 1 times
Followed by:1 members

by f2001290 » Tue May 29, 2007 10:18 pm
If 1st digit is zero, then it becomes a 3 digit number.

0123 is a 3 digit number.

Rags, I may be wrong (most of the time) :wink: . The most unfortunate thing is that I don't have an OA
Top
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 am
Location: India
Thanked: 51 times
Followed by:1 members

by gabriel » Wed May 30, 2007 8:46 am
... i agree with RAGS ... 0 can be the first number .. wen u say that 0 as the first number wuld reduce it to a 3 digit number .. that is only true wen u consider the numerical value of the 4 digit number ... over here the numerical value is not important but the combination of different numbers is.. so 0 can be the first number ... btw my bag which had a number lock used to open with a 0000 :D
Top
Post new topic Post Reply
• Page 1 of 1