# Four balls are numbered 1 through 4 and placed in a box. Two balls are selected without replacement. Find the probability thatA. the sum of the numbers is even.B. the number on the second ball is less than the number on the first ball.C. the sum of the numbers on both balls is greater than 3.

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Four balls are numbered 1 through 4 and placed in a box. Two balls are selected without replacement. Find the probability that

A. the sum of the numbers is even.

B. the number on the second ball is less than the number on the first ball.

C. the sum of the numbers on both balls is greater than 3.

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Step 1

We have four balls are numbered 1 through 4 and placed in a box.

Now, we are going to select 2 balls without replacement.

So,  The total number of cases will be 12 which is  (12,13,14,21,23,24,31,32,34,41,42,43).

Step 2

(a) The sum of the even number ( 1+3,3+1,2+4,4+2)=4

So, the favorable case will be 4.

Probability shown below:

Step 3

(b) The total number of cases for the number on the second ball is less tha...

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