Question

In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of not getting a prize?
(a) $\dfrac{1}{10}$
(b) $\dfrac{2}{5}$
(c) $\dfrac{2}{7}$
(d) $\dfrac{5}{7}$

Answer 1

Hint: For this problem, we have 10 numbers of prizes and 25 blanks tickets. So, the total number of lottery tickets is 35 (10 prizes and 25 blanks). So, we have both the favorable as well as the total outcome. Hence, we can calculate the probability of the event easily.

Complete step-by-step answer:
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. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty
In this question, first we calculate the total number of tickets. There are 10 numbers of prizes and 25 blanks tickets. So, the total number of lottery tickets is 35 (10 prizes and 25 blanks). Using this data, we can calculate the probability of the event easily. Therefore,
Total number of prizes $=10$.
The total number of blanks $=25$.
The total number of tickets $=10+25=35$.
Therefore, 25 times out 35, a prize is won.
E be the event of drawing a lottery ticket.
Formula of probability of any event,$P\left( E \right)=\dfrac{Number\text{ of favourable outcomes}}{Total\text{ number of possible outcomes}}$
Here, the number of favorable outcomes = 25.
Total number of outcomes = 35.
P (Not getting a prize)$=\dfrac{25}{35}$
P (Not getting a prize)$=\dfrac{5}{7}$.
Hence, the probability of not getting a prize is $\dfrac{5}{7}$.
Therefore, option (d) is correct.

Note: This problem can be alternatively be solved by using another approach for probability. First, we can calculate the probability of getting a prize and then subtract this value from 1 to get the final answer. Both of the approaches are correct.