Question

In a lottery, there are 5 prized tickets and 995 black tickets. A person buys a lottery ticket. Find the probability of his winning a prize.

Answer 1

In this type of question we have to use the concept of probability. We know that probability is the measure of possibility of occurrence of an event. The value of probability always ranges from 0 to 1. If the probability equals 0 it means the event is an impossible event while probability equals to 1 means the event is a certain event. We can calculate the probability of an event by using the ratio of the number of favourable outcomes to the total number of outcomes. Hence we can write it as $\text{Probability of an event = }\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

Complete step by step solution:
Now here we have to find the probability of winning a prize.
We have given that,
Number of prized tickets = 5
Number of black tickets = 995
Hence, Total number of tickets = 1000
As we have to find the probability of a person of winning a prize,
The number of favourable outcomes = Number of prized tickets
Thus, Number of favourable outcomes = 5
Thus we can find the probability as
$\Rightarrow \text{Probability of winning a prize = }\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

& \Rightarrow \text{Probability of winning a prize = }\dfrac{\text{5}}{\text{1000}} \\\ & \Rightarrow \text{Probability of winning a prize = 0}\text{.005} \\\ \end{aligned}$$ **Hence, the probability of his winning is 0.005** **Note:** In this type of question students may make mistakes in finding the probability. Students have to take care of the total number of tickets which is in addition to prized tickets and black tickets. Also students have to take care when they divide 5 by 1000.