Question

In mathematics Exam, the probability of Aayushi scoring 100 out of 100 is:
(a) 1
(b) 0
(c) \[\dfrac{1}{100}\]
(d) \[\dfrac{1}{101}\]

Answer 1

Hint: In order to find the solution to this question, we should know about the concept of the probability that is, the ratio of favorable outcomes to the total number of outcomes of any event. Mathematically, we can write, the probability of an event \[=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}.\] By using this concept, we can find the answer to this question.

Complete step-by-step answer:
In this question, we have been asked to find the probability of Aayushi scoring 100 out of 100. To solve this question, we should know about the concept of probability, that is, the ratio of the favorable outcomes to the total number of outcomes. Therefore, we can say,
 \[\text{Probability of an event}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\]
Now, we have been given that the maximum marks Aayushi can score is 100. But we know that Aayushi can also have a score of 0 marks, 1 mark, 2 marks, 3 marks, ….., 100 marks, that is, there are 101 possibilities. So, we can say the total number of favorable outcomes is 101. Now, we have been given that we have to find the probability to get 100 marks. So, we have only 1 possible mark, which is 100 marks. Therefore, we can say that there is 1 favorable outcome. So, we can say the portability of Aayushi scoring 100 out of 100 marks is
\[\text{Probability Aayushi scoring 100 out of 100 marks}=\dfrac{1}{101}\]
Hence, we can say that the probability of Aayushi scoring 100 out of 100 marks is \[\dfrac{1}{101}.\] Therefore, we can say option (d) is the right answer.

Note: While solving this question, the possible mistake one can make is counting the total number of outcomes as 100 by not including 0 marks as the outcome. But we know that in an exam, one can also score 0 marks. Therefore, there are 101 outcomes in total.