Question

A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
A) 40
B) 240
C) 480
D) 750

Answer 1

In the above question we will use the basic concept of probability. And also, we use the basic formula of probability.
Probability of event happen P(E) = $\dfrac{{Number\,of\,favourable\,condition}}{{total\,number\,of\,outcomes}}$

Complete step by step solution:
Probability of winning the first prize P(E) = 0.08
Total number of tickets sold (T) = 6000
Now, let the number of tickets she bought = X
Then, P(E) = $\dfrac{X}{T}$
Where, X = number of tickets and T = total number of tickets sold
Putting the values in the formula:
We get, 0.08 = $\dfrac{X}{{6000}}$
$X = 0.08 \times 6000 --- \text{cross multiplying} \\\ \Rightarrow X = \dfrac{8}{{100}} \times 6000 \\\ \Rightarrow X = 480$
Therefore, number of tickets she bought = 480

The correct option is C.

Note:
Students can solve this question with an alternative method. Let’s see how we can solve it.
Probability of winning 1st prize = 0.08 =$\dfrac{8}{{100}}$
Probability of winning 1st prize = $\dfrac{{Number\,of\,tickets\,bought}}{{Total\,number\,of\,tickets}}$
Number of tickets bought = $\dfrac{8}{{100}} \times 6000$
$\Rightarrow$480 tickets
Hence, she bought 480 tickets.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The probability of all the events in a sample space adds up to 1.
For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But if we toss coins in the air, there could be three possibilities of events to occur, such as both the coins show heads or both the coins shows tails or one shows heads and one tails, i.e. (H, H), (H, T), (T, T).