Question

Whenever horses $a,b,c$ race together, their respective probabilities of winning the race are $0.3,0.5$ and $0.2$ respectively. If they race three times the probability that "the same horse wins all the three races" and the probability that $a,b,c$ each wins one race, are respectively (Assume no dead heat)

• A. $\frac{8}{50};\frac{9}{50}$
• B. $\frac{16}{100};\frac{3}{100}$
• C. $\frac{12}{50};\frac{15}{50}$
• D. $\frac{10}{50};\frac{8}{50}$

Answer 1

Answer: (A)

$\frac{8}{50};\frac{9}{50}$

horses: $a,b,c$

$P\left(a\right)=0.3$

$P\left(b\right)=0.5$

$\left(c\right)=0.2$

either $a,b$ or $c$ can will all

$\Rightarrow (0.3{)}^3+(0.5{)}^3+(0.2{)}^3$

$\Rightarrow \frac{27}{1000}+\frac{125}{1000}+\frac{8}{1000}$

$=\frac{160}{1000}=\frac{8}{50}$

now each can win one race

$\therefore$ Total ways of happening $\Rightarrow 3!$

$=3\times 2\times 1$

$=6$ ways

$\therefore$ probability $\Rightarrow 6\times \left(0.3\right)\left(0.5\right)\left(0.2\right)$

$\Rightarrow 6\times \frac{30}{1000}$

$=\frac{9}{50}$

option $A$