Question

In a cricket team there are 4 batsmen, 5 bowlers, and 2 all-rounders. One player is chosen at random, what is the probability that the chosen player is an all-rounder?
A. $\dfrac{4}{{11}}$
B. $\dfrac{5}{{11}}$
C. $\dfrac{2}{{11}}$
D. $\dfrac{1}{{11}}$

Answer 1

We find the total number of players in the cricket team by adding the numbers of players of each kind which will be the total outcomes. Now for an all-rounder, there are only 2 all-rounders. So, it is a favorable outcome. After that using the formula of probability, we find the probability of the chosen player to be an all-rounder.

Complete step by step answer:
The probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.
We are given a cricket team.
The number of batsmen in the team is 4.
The number of bowlers in the team is 5.
The number of all-rounders in the team is 2.
The total number of players in the team is given by the addition of the number of players of each type which will be the total outcomes,
$\Rightarrow n\left( S \right) = 5 + 4 + 2$
Add the terms on the right side,
$\Rightarrow n\left( S \right) = 11$
Now, the probable outcome is given by the number of all-rounder players,
$\Rightarrow n\left( E \right) = 2$
Now, substitute the values in probability formula,
$\Rightarrow$ Probability $= \dfrac{2}{{11}}$
Thus, the probability is $\dfrac{2}{{11}}$.

Hence, option (C) is the correct answer.

Note: Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
$P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$
A probability of 0 means that an event is impossible.
A probability of 1 means that an event is certain.
An event with a higher probability is more likely to occur.
Probabilities are always between 0 and 1.