Question

A gumball machine contains 40 blue gum balls, 20 red gumballs, 15 white gumballs and 25 purple gumballs. What is the probability that a person gets a red gumball?
A. 0.10
B. 0.20
C. 0.25
D. 0.15

Answer 1

Hint: To solve this question, we should know about probability. If n is the total number of outcomes in the sample space and m is the number of favourable outcomes, then the probability of getting the favourable outcome is given by the formula, $P={\displaystyle \frac{m}{n}}$ . We will use this concept to find the probability of getting a red gumball from the gumball machine.

Complete step-by-step answer:
In the question given to us, we are given the sample space as a gumball machine with different coloured gumballs, which are blue gumballs, red gumballs, white gumballs and purple gumballs respectively. We have also been given the count of these different coloured gumballs as follows,

The number of blue gumballs = 40
The number of red gumballs = 20
The number of white gumballs = 15
The number of purple gumballs = 25
So, we can get the total outcomes, that is the gumballs in the sample space, n as,
 $n=40+20+15+25=100$ .
Now, we have been asked to find the probability of getting a red gumball, which can be given as follows,
 $P\left(\text{red gumballs}\right)={\displaystyle \frac{\text{ total number of red gumballs}}{\text{total number of gumballs}}}$
So, here we have the number of red gumballs as 20 and the total number of gumballs as 100. So, we get,
 $\begin{array}{rl}& P\left(\text{red gumballs}\right)={\displaystyle \frac{20}{100}}\\ & \Rightarrow P\left(\text{red gumballs}\right)=0.2\end{array}$
So, we get the probability of getting a red gumball as 0.2.
Therefore, the correct answer is option B.

Note: We should always remember that the probability of an event can never be negative, so one can recheck their answer if they get a negative value. The probability of an event is always between 0 and 1. Some students may make mistakes in the final step while finding the decimal value, they may write ${\displaystyle \frac{20}{100}}=2.00$ instead of 0.2. So such mistakes must be avoided. The answer can also be written in the fraction.