Question & Answer
QUESTION

A bag contains 5 red balls, 7 black balls and 8 green balls. A ball is drawn randomly from the bag, the probability of getting a red ball is $\dfrac{1}{m}$. Then find the value of m.

ANSWER Verified Verified
Hint: Find the total number of balls or total outcomes and the number of red balls or favourable outcomes. Then use the formula $P\left( A \right)=\dfrac{\text{No. of favourable outcomes}}{\text{Total no. of outcomes}}$ and put the values we found before in this to find the final answer.

Complete step-by-step answer:

In this question, we are given that a bag contains 5 red balls, 7 black balls and 8 green balls. A ball is drawn randomly from the bag, the probability of getting a red ball is $\dfrac{1}{m}$.

We need to find the value of m.

Let us write the definition of probability.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. Probability is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility and 1 indicates certainty.

For an event A, the probability of the event A to occur is:
$P\left( A \right)=\dfrac{\text{No. of favourable outcomes}}{\text{Total no. of outcomes}}$

In our question,
Total number of balls or total outcomes = 5 + 7 + 8 = 20
The number of red balls or favourable outcomes = 5
So, probability of getting a red ball = $\dfrac{5}{20}=\dfrac{1}{4}$
So, the value of m is equal to 4.

This is our final answer.

Note: In this question, it is very important to know the concept and definition of probability. For an event A, the probability of the event A to occur is $P\left( A \right)=\dfrac{\text{No. of favourable outcomes}}{\text{Total no. of outcomes}}$. Note here that the total number of outcomes are not 3 for the number of colours but 20 for the number of balls. Similarly, Number of favourable outcomes are not 1 for red colour but 5 for number of red balls.