Question

A bag contains 12 balls out of which x are white. If one ball is drawn at random, what is the probability that it will be a white ball?
\[\left( a \right)x\]
\[\left( b \right)\dfrac{x}{2}\]
\[\left( c \right)\dfrac{x}{12}\]
\[\left( d \right)12x\]

Answer 1

Hint: We have a total of 12 balls out of which x are white. We know that the probability is defined as the ratio of favorable outcomes to the total outcomes. We will see that the total outcomes are 12 as 12 balls are there in total while the possible outcomes are x as x white balls are there, then we put in the formula defined above and get our solution.

Complete step-by-step solution:
We are asked to find the probability of picking a ball out of a bag. We know that the probability in the description which tells us about how likely an event is to occur. Probability is given by the formula defined as
\[\text{Probability of event x}=\dfrac{\text{Number of favourable outcomes for x}}{\text{Total Possible Outcomes}}\]
We are given that a bag contains 12 balls of a different color. We are picking a random ball from the bag. As there are 12 balls in the bag, so we can choose a ball from these 12 only, and hence only 12 balls can be taken out one after the other. This means that we have a total possible outcome of 12.
Now, we are looking for the case when white is drawn. As we have that a total of x white are there, this means that when we pick a ball, then white ball occurs out of these x balls. So, our favorable outcome that is choosing a white ball occurs x times as there are only x white balls. So,
Number of favorable outcome = x
Now, we will use our formula,
\[\text{Probability of white ball be chosen}=\dfrac{\text{Number of favourable outcomes}}{\text{Total Possible Outcomes}}\]
Favourable outcomes = Choosing white ball = x and Total outcome = 12
So, we get,
\[\text{Probability of choosing white ball}=\dfrac{x}{12}\]
Hence, the correct option is (c).

Note: Students need to remember that in probability, we do not look at how many balls are chosen at a time. We look for how many possibilities we have to choose from. If we are choosing a white ball and we took 1 at a time and there are a total of x ball, so we have a choice of choosing only 1 from those x balls. So, the number of favorable outcomes will be x here. A mistake can be made by misinterpreting the question and taking the total number of balls as 12+x instead of 12. So, this must be avoided.