Question

Three players : A, B & C are associated in a race,. If the probability that A wins equals double that of B & the probability that B wins equals that of C.
Find thre probabiltiy that B or C wins, given that only one players wins this race.

Answer 1

total probability always equals 1
so, pA+pB+pC =1
also it is given that pA=2pB, and pB=pC
can u find pB , pC now ?

Answer 2

Wow!! Yes. Thank you so much, Sir. I appreciate your help.

Answer 3

remember for B or C, you need to add, pB+pC

\[ \begin{array}l\color{red}{\text{w}}\color{orange}{\text{e}}\color{#e6e600}{\text{l}}\color{green}{\text{c}}\color{blue}{\text{o}}\color{purple}{\text{m}}\color{purple}{\text{e}}\color{red}{\text{ }}\color{orange}{\text{^}}\color{#e6e600}{\text{_}}\color{green}{\text{^}}\color{blue}{\text{}}\end{array} \]

Answer 4

Yes, you're right. Thanks again.
One last questions, though. Does the given "only one wins this race" affect the way of solving this? I mean if it didn't say, this should be the same solution right?

Answer 5

it affects, for this A 'and' B = 0
same for B 'and' C = 0 , A and C =0
if that was not given, then this question becomes too complex to solve.

Answer 6

:) Well that's it then, Thanks for your time, Sir. :)

Answer 7

\[ \begin{array}l\color{red}{\text{w}}\color{orange}{\text{e}}\color{#e6e600}{\text{l}}\color{green}{\text{c}}\color{blue}{\text{o}}\color{purple}{\text{m}}\color{purple}{\text{e}}\color{red}{\text{ }}\color{orange}{\text{^}}\color{#e6e600}{\text{_}}\color{green}{\text{^}}\color{blue}{\text{}}\end{array} \]