NIMCET 2018 — Mathematics PYQ

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Question

NIMCET 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial, is:

Choose the correct answer:

Explanation

**Concept:**

• The **probability** of the occurrence of an event A out of a total possible outcomes N, is given by:
$P (A) = \frac{n ( A )}{N}$ , where $n (A)$ is the number of ways in which the event A can occur.

• $P (not A) = 1 - P (A)$

• **Basic Principle of Counting:**
If there are m ways for happening of an event A, and corresponding to each possibility there are n ways for happening of event B, then the total number of different possible ways for happening of events A and B are:
○ Either event A alone **OR** event B alone: $m + n$
○ Both event A **AND** event B together: $m \times n$

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**Calculation:**

The total number of possible pairs of selected numbers = $N = 25 \times 25 = 625$

If the numbers match, then both the numbers should be (1, 1), (2, 2), ... and so on.

Let's say that A is the event that both the selected numbers match.

The number of possible cases where the numbers match = $n (A) = 25$

And,
$P (A) = \frac{n ( A )}{N} = \frac{25}{625} = \frac{1}{25}$

∴ Probability that the numbers will not match = $1 - P (A) = \frac{24}{25}$

Hence, the probability of not winning a prize is $\frac{24}{25}$ .