Question

A cricket team plays $x$ number of matches in winter and wins $m$ matches. Further it plays $y$ number of matches in summer and wins $n$ matches. Its winning probability in both the seasons is.
A. $\dfrac{m}{x} \cdot \dfrac{n}{y}$
B. $\dfrac{x}{m} - \dfrac{y}{n}$
C. $\dfrac{{m + n}}{{x + y}}$
D. $\dfrac{{x + y}}{{m + n}}$

Answer 1

Hint : The probability of occurrence of an event is given by given by, $P\left( A \right) = \dfrac{a}{b}$ , where $a =$ number of favorable outcomes and total number of outcomes.

Complete step-by-step answer :
Winter season:
The number of matches played by the team during the winter season $= x$
Number of matches won by the team in that period $= m$
Therefore, number of favorable outcomes for winning in winter season is $m$
Summer Season:
The number of matches played by the team during the winter season $= y$
Number of matches won by the team in that period $= n$
Therefore, number of favorable outcomes for winning in summer season is $n$
In order to calculate the probability of winning in both the seasons, the total matches won by the team in both the seasons and total number of matches played is to be added separately.
Total number of matches played in the month during the winter and summer season is,
$N = x + y \cdots \left( 1 \right)$
Total number of favorable outcomes for winning the match in that period is ,
$M = m + n \cdots \left( 2 \right)$
Probability of winning in both seasons is given by,
$P\left( W \right) = \dfrac{M}{N} \cdots \left( 3 \right)$
Substitute the value of $M$ and $N$ from equation (1) and (2) in equation (3),
$P\left( W \right) = \dfrac{{m + n}}{{x + y}}$
So, the correct answer is “Option C”.

Note : The probability is the chances of occurrence of an event. It tells how likely the event is bound to happen.
The probability of a sure event is $1$ .
The formula for calculation of probability of an event is given by,
$P(A) = \dfrac{m}{N}$
Where,
$m =$ Total number of favorable outcomes.
$N =$ Total number of outcomes.