Question

A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that the ball drawn is white?

Answer 1

We use the concept of probability to solve the above question. We need to use the formula for probability which is given by the number of favourable outcomes divided by the number of total outcomes in any event. Here, we need to divide the number of ways in which we can get a white ball divided by the total number of ways we can get any ball out.

Complete step-by-step answer:
To solve this question, we first explain the concept of probability. Probability can be defined as the likeliness of a particular event to occur. This is usually given by a formula such that in order to find the required probability, we divide the number of favourable outcomes divided by the total number of outcomes in any event.
$\Rightarrow \text{Probability=}\dfrac{\text{Total number of favorable events}}{\text{Total number of outcomes in the event}}$
For the above question, it says that one ball is drawn from a bag of 5 white and 7 red balls. Therefore, the total number of balls in the bag are 12 and we can say that if we are to draw a random ball from this, we can do this in 12 ways. This means that the total number of outcomes is 12.
$\Rightarrow \text{Total number of outcomes in the event}=12$
Now, we can get a white ball which can only be drawn from the 5 white balls in the bag. Hence, the number of favourable events is 5.
$\Rightarrow \text{Total number of favorable events=5}$
Now we find the probability using the above formula.
$\Rightarrow \text{Probability=}\dfrac{\text{Total number of favorable events}}{\text{Total number of outcomes in the event}}=\dfrac{5}{12}$
Hence, the probability that the ball drawn is white is $\dfrac{5}{12}.$

Note: It is important to know the concept of probability to solve such questions. We need to note that the sum of all probabilities of an event always adds up to 1. In case it does not, then there must be something wrong in the solution. This is an important way to check if we have arrived at the right solution. For example, for the above question, the probability of obtaining a red ball is $\dfrac{7}{12},$ and the sum of this probability with the probability of obtaining a white ball adds up to 1 showing that it is correct.