Question

Two cards are drawn at random from 10 cards numbered 1 to 10. The probability that their sum is odd if both the cards are drawn together

• A. $\frac{1}{3}$
• B. $\frac{4}{9}$
• C. $\frac{5}{9}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{5}{9}$

The number of ways of choosing one odd and one even number is ${}^5{C}_1{\times }^5{C}_1=5\times 5=25$
Total number of ways of choosing 2 cards out of 10${=}^{10}{C}_2=45$
Thus, probability $=25/45=5/9$