Question

From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21 21 21

Answer 1

Explanation:

We know that between 1 to 10 there are 5 even and 5 odd numbers.

We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards

Let´s check all this combinations

Case 1: When all 4 numbers are even:

We are going to take 4 of the 5 even numbers in the box so we have

`5C4=5`

Case 2: When all 4 numbers are odd:

We are going to take 4 of the 5 odd numbers in the box, so we have

`5C4=5`

Case 3: When 2 are even and 2 are odd:

We are giong to take 2 from 5 even and odd cards in the box so we have

`5C2 * 5C2`

Remember that we obtain the probability from

`(Number-of-favourable-Outcome)/(Total-number-of-outcomes)`

So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:

We are taking 4 of the 10 cards:

`10C_4=210`

Hence we have that the probability that their sum is even

`(5+5+100)/(210)=(11)/(21)`