Question

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

• A. $\frac{11}{21}$
• B. $\frac{5}{21}$
• C. $\frac{6}{21}$
• D. $\frac{1}{21}$

Answer 1

Answer: (A)

$\frac{11}{21}$

Between 1 to 10 there are 5 even and 5 odd numbers.
We could get sum of 4 drawn cards even for following cases:
Case 1: When all 4 numbers are even: ${}^5{C}_4=5$ (select any 4 even numbers out of total 5 even numbers)
Case 2: When all 4 numbers are odd: ${}^5{C}_4=5$ (select any 4 odd numbers out of total 5 odd numbers)
Case 3: When 2 are even and 2 are odd: ${}^5{C}_2\times {}^5{C}_2=100$
Total cases for drawing four cards are: ${}^{10}{C}_4=210$ (select any 4 out of total 10)
Hence, probability that sum is even $=\frac{5+5+100}{210}=\frac{11}{21}$