9 balls labelled 1 - 9 are placed within a jar and two are pulled at

Question

9 balls labelled 1 - 9 are placed within a jar and two are pulled at random without replacement. What is the probability that the sum of the numbers on those two balls will be even?

A. 16/81
B. 25/81
C. 4/9
D. 41/81
E. 5/9

doomedcat · Accepted Answer

We can get Even sum in two cases

ODD + ODD = EVEN 
 EVEN + EVEN = EVEN

Case 1) Two ODD numbers are picked

P(First Number to be ODD) and P(2nd Number be ODD  =  \frac{5}{9}*\frac{4}{8}  =   \frac{20}{72}

Case 2) Two Even number are selected

P(First Number to be EVEN) and P(2nd Number be EVEN  =  \frac{4}{9}*\frac{3}{8}  =   \frac{12}{72}

Total Probability :  \frac{20}{72}+\frac{12}{72}  =   \frac{4}{9}

pr3mk5 · Answer

For the sum to be even both the numbers should be odd or even.

Odd numbers (1,3,5,7,9) = 5 numbers
Even Numbers (2,4,6,8) = 4 numbers

Odd + odd will be: 5 * 4
Even + even will be: 4 * 3
Selecting two numbers will be: 9 * 8

So, probability of selecting two numbers = ((5*4) + (4*3))/(9*8) = 4/9

OA - C.

blueviper · Answer

Total ways to select 2 balls from the jar = 9p2 = 9!/7! = 9 x 8 = 72

Favorable cases = 5 x 4 + 4 x 3 = 32

P(E) = Facorable Cases / Total ways = 32 / 72 = 4/9. Answer is C.

ADisHere · Answer

I cant understand why am i wrong.

favourable outcomes
  
4 evens and 5 odds
hence selected 4E + 4E = 8
and 5O+ 5O = 10

hence  favourable outcomes = 18

Now from 9 balls, we have to select 2 without replacement hence 9C2= 36

So why isn't the answer 1/2

Bunuel · Answer

The issue is with how you calculated the number of ways to pick 2 odd and 2 even balls. The correct calculation is:

The number of ways to pick 2 odd-numbered balls from 5 is 5C2 = 10. 
 The number of ways to pick 2 even-numbered balls from 4 is 4C2 = 6.

Thus, the total favorable outcomes are 10 + 6 = 16.

The total ways to select 2 balls from 9 is 9C2 = 36.

The probability is therefore 16/36 = 4/9.

9 balls labelled 1 - 9 are placed within a jar and two are pulled at

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9 balls labelled 1 - 9 are placed within a jar and two are pulled at

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