Ten strips of paper are numbered from 1 to 10 and placed in a bag. If

Question

Ten strips of paper are numbered from 1 to 10 and placed in a bag. If three numbers are drawn from the bag at random, what is the probability that the sum of the numbers drawn will be odd?

A. 1/12
B. 5/36
C. 15/36
D. 1/2
E. 11/18

Archit3110 · Accepted Answer

possible ways to get sum odd of three numbers from 1 to 10
all are odd or two are even and 1 is odd
total ways to select 10c3 ; 120
all are odd ; 5c3 ; 10
two even and 1 odd ; 5c2 * 5c1 ; 50
total ways ; 10+50 ; 60
60/120 ; 1/2
option D

Bunuel · Answer

PyjamaScientist · Answer

The sum of the three numbers on the strips of paper selected from the box to be odd one should select either three odd-numbered strips of paper (Odd+Odd+Odd=Odd) or two even-numbered strips of paper and one odd-numbered strip of paper (Even+Even+Odd=Odd) ;

P(OOO) =  \frac{5}{10}*\frac{4}{9}*\frac{3}{8} = \frac{1}{12} ;

P(EEO) =  3*(\frac{5}{10}*\frac{4}{9}*\frac{5}{8})= \frac{5}{12}  (you should multiply by 3 as the scenario of two even-numbered strips of paper and one odd-numbered strip of paper can occur in 3 different ways: EEO, EOE, or OEE); or simply  \frac{3!}{2!}

So finally  P=\frac{1}{12}+\frac{5}{12}=\frac{1}{2} .
 Option (D).

GMATcracker101 · Answer

This is a trick question meant to take your time out for calculations.

Ten strips of paper are numbered from 1 to 10 and placed in a bag. If three numbers are drawn from the bag at random, what is the probability that the sum of the numbers drawn will be odd?

3 numbers are drawn - we can do this the lengthy way by calculating the probability of all numbers being ODD or 2 being EVEN and 1 being ODD.

Or we can simply understand that the sum of the three numbers will either be EVEN or it will be ODD. There is a 50/50 chances of either occurence as there are 5 ODD and 5 EVEN numbers.

tanvi0915 · Answer

Can someone let me know if this method is correct???

I realised the Probability of getting an even number is 5/10 = 1/2 and Probability of getting an odd number = 1/2
Therefore Cases in this question are P(oee) or P(ooo)
= (1/2)*(1/2)*(1/2)*3!/2! + (1/2)*(1/2)*(1/2)*3!/3!
= 3/8+1/8
=4/8
= 1/2

Bunuel · Answer

No, your method is not correct because this is not a with-replacement scenario. With this method, the correct approach is shown just  two posts above yours . Please review the thread before posting.

Ten strips of paper are numbered from 1 to 10 and placed in a bag. If

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Ten strips of paper are numbered from 1 to 10 and placed in a bag. If

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