Algebra

Probability

Medium

core

In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is $\frac{m}{n}$ , gcd(m, n) = 1, then m + n is equal to

✅ Correct Option: 1

The class has equal numbers of boys and girls, with 5% of boys and 0.25% of girls physically fit. A fit student is selected at random, and we need to find the probability that the selected student is a girl.

Let there be $n$ boys and $n$ girls in the class.

Number of fit boys:

$\frac{5}{100} \times n$

$= \frac{n}{20}$

Number of fit girls:

$\frac{0.25}{100} \times n$

$= \frac{1}{400} \times n$

$= \frac{n}{400}$

Total number of fit students:

$\frac{n}{20} + \frac{n}{400}$

Converting to common denominator:

$= \frac{20n}{400} + \frac{n}{400}$

$= \frac{21n}{400}$

The probability that the selected fit student is a girl:

$P(\text{girl | fit}) = \frac{\text{Number of fit girls}}{\text{Total fit students}}$

$= \frac{\frac{n}{400}}{\frac{21n}{400}}$

$= \frac{n}{400} \times \frac{400}{21n}$

$= \frac{1}{21}$

The probability is $\frac{1}{21}$ where $m = 1$ and $n = 21$ .

Since $\gcd(1, 21) = 1$ , the answer is:

$m + n = 1 + 21 = 22$

2026: 12 May Shift 2

From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random. Let X denotes the number of defective items in the sample. If the sample is drawn randomly, then Match List-I with List-II (P(X) denotes the probability of occurence of X)

List-I	List-II
(A) P (X = 0)	(I) $\dfrac{^3C_3\times{}^7C_1}{^{10}C_4}$
(B) P (X = 1)	(II) $\dfrac{^7C_4\times{}^3C_0}{^{10}C_4}$
(C) P (X = 2)	(III) $\dfrac{^3C_1\times{}^7C_3}{^{10}C_4}$
(D) P (X = 3)	(IV) $\dfrac{^3C_2\times{}^7C_2}{^{10}C_4}$

Choose the correct answer from the options given below:

2026: 18 May Shift 2

If $P(A) = 0.4$ , $P(B) = X$ and $P(\bar{A} \cap \bar{B}) = 0.4$ , where A and B are independent event, then the value of X is:

2024: 16 May Shift 1

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and the second throw of dice and a number less than $4$ in the third throw ?

2026: 12 May Shift 2

A die is thrown once then,

Match List-I with List-II

List-I	List-II
(A) Probability of getting odd number	(I) $\dfrac{1}{3}$
(B) Probability of getting number more than 4	(II) $\dfrac{2}{3}$
(C) Probability of getting number less than or equal to 4	(III) $\dfrac{1}{2}$
(D) Probability of getting number 2	(IV) $\dfrac{1}{6}$

Choose the correct answer from the options given below:

2025: 13 May Shift 1

Let E and F are events associated with an experiment. If $P(E) = 0.4$ , $P(F) = 0.8$ and $P(F|E) = 0.6$ , then $P(E|F)$ is

2026: 30 May Shift 2

If A and B are two independent events such that P(A) = 1/3, $P(A\cup B) = 3/5$ and P(B) = p, then which of the following are true?

(A) The value of p is $\frac{2}{5}$

(B) $P(A\cap B) = \frac{2}{15}$

(D) $P(A/B) = \frac{3}{5}$

Choose the correct answer from the options given below:

In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is mn\frac{m}{n}nm​, gcd(m, n) = 1, then m + n is equal to

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CUET Mathematics Past Year Questions (Topic-Wise)

In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is $\frac{m}{n}$ , gcd(m, n) = 1, then m + n is equal to