Answer:
Step-by-step 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](https://tex.z-dn.net/?f=5C4%3D5)
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](https://tex.z-dn.net/?f=5C4%3D5)
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](https://tex.z-dn.net/?f=5C2%20%2A%205C2)
Remember that we obtain the probability from
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](https://tex.z-dn.net/?f=10C_4%3D210)
Hence we have that the probability that their sum is even
![\frac{5+5+100}{210}=\frac{11}{21}](https://tex.z-dn.net/?f=%5Cfrac%7B5%2B5%2B100%7D%7B210%7D%3D%5Cfrac%7B11%7D%7B21%7D)