Question

There are $2$ people who are going to take part in race. The probability that the first one will win is $\frac{2}{7}$ and that of other winning is $\frac{3}{5}$. What is the probability that one of them will win?

Answer 1

Probablity (First $\to$Win)=$\frac{2}{7}$

Probablity (Second $\to$Win)=$\frac{3}{5}$

Probablity (First $\to$Lose)=$\frac{5}{7}$

Probablity (Second$\to$Lose)=$\frac{2}{5}$

Probablity that one of them will win = $\frac{2}{7}$ $\times$ $\frac{2}{5}$ + $\frac{3}{5}$ $\times$ $\frac{5}{7}$= $\frac{19}{35}$