Question

Amar, Bimal, and Chetan are three contestants for an election, odds against Amar will win is $4:1$and odds against Bimal will win is $5:1$ and the odds in favor of Chetan will win $2:3$ then what is the probability that either Amar or Bimal or Chetan will win the election.

• A. $\frac{23}{20}$
• B. $\frac{11}{30}$
• C. $\frac{7}{10}$
• D. None of these

Answer 1

The correct option is D

None of these

Finding the probability:

The probability that Amar will win the tournament is $P\left(A\right)=\frac{1}{5}$

The probability that Bimal will win is $P\left(B\right)=\frac{1}{6}$

The probability that Chetan will win is $P\left(C\right)=\frac{2}{5}$

Since these events are mutually exclusive.

$\begin{array}{rcl}P(A\cup B\cup C)& =& P\left(A\right)+P\left(B\right)+P\left(C\right)\\ & =& \frac{1}{5}+\frac{1}{6}+\frac{2}{5}\\ & =& \frac{6+5+12}{30}\\ & =& \frac{23}{30}\end{array}$

Hence, option (D) is the correct answer.