Question

In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize?

Answer 1

Hint: Here, we will proceed by using the general formula for calculating the probability of occurrence of an event i.e., Probability of occurrence of an event $ = \dfrac{{{\text{Number of favourable cases}}}}{{{\text{Total number of possible cases}}}}$ and here the favourable event will be getting a prize.

Complete Step-by-Step solution:
Given, Number of prizes in the lottery = 10
Number of blanks in the lottery = 25
As we know that the general formula for probability of occurrence of an event is given by
Probability of occurrence of an event $ = \dfrac{{{\text{Number of favourable cases}}}}{{{\text{Total number of possible cases}}}}{\text{ }} \to {\text{(1)}}$
Here, we have to find the probability of getting a prize so the favourable event is getting a prize.
Here, Total number of possible cases = (Number of prizes in the lottery)+(Number of blanks in the lottery)
$ \Rightarrow $Total number of possible cases = 10+25 = 35
Number of favourable cases = Number of prizes in the lottery = 10
By substituting the obtained values in equation (1), we get
Probability of getting a prize $ = \dfrac{{{\text{10}}}}{{{\text{35}}}} = \dfrac{2}{7}$
Therefore, the required probability of getting a prize in the lottery is $\dfrac{2}{7}$.

Note: In this particular event, if instead of probability of getting a prize we are asked for the probability of getting a blank (i.e., not getting any prize). For that case, the favourable event will be getting a blank from there the probability of getting a blank will be equal to $\dfrac{{25}}{{35}} = \dfrac{5}{7}$. Here, if we see carefully the sum of the probabilities of getting a prize and getting a blank will always be equal to 1.