Question

the probability of a horse A winning a race is 1/5 and the probability of a horse B of winning the race is 1/4.what is the probability that (1) either of them will win (2) none of them will win ?

Answer 1

$$\begin{gathered} \mathrm{Probability}\mathrm{of}\mathrm{A}\mathrm{winning}\mathrm{the}\mathrm{race}=\frac{1}{5} \\ \mathrm{Probability}\mathrm{of}\mathrm{A}\mathrm{not}\mathrm{winning}\mathrm{the}\mathrm{race}=1-\frac{1}{5}=\frac{4}{5} \\ \mathrm{Probability}\mathrm{of}\mathrm{B}\mathrm{winning}\mathrm{the}\mathrm{race}=\frac{1}{4} \\ \mathrm{Probability}\mathrm{of}\mathrm{B}\mathrm{not}\mathrm{winning}\mathrm{the}\mathrm{race}=1-\frac{1}{4}=\frac{3}{4} \\ \mathrm{So}\mathrm{probability}\mathrm{that}\mathrm{either}\mathrm{of}\mathrm{them}\mathrm{win} \\ =\mathrm{A}\mathrm{win}\mathrm{B}\mathrm{lose}+\mathrm{B}\mathrm{win}\mathrm{A}\mathrm{lose}+\mathrm{both}\mathrm{win} \\ =\frac{1}{5}\times \frac{3}{4}+\frac{1}{4}\times \frac{4}{5}+\frac{1}{4}\times \frac{1}{5} \\ =\frac{8}{20} \\ \mathrm{Noe}\mathrm{of}\mathrm{them}\mathrm{win}=\mathrm{Alose}\mathrm{B}\mathrm{lose}=\frac{4}{5}\times \frac{3}{4}=\frac{12}{20} \end{gathered}$$