Algebra

Probability

Medium

core

A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem is solved is

3/4

1/3

1/6

✅ Correct Option: 1

The problem involves three students attempting to solve independently with probabilities $\frac{1}{2}$ , $\frac{1}{3}$ , and $\frac{1}{4}$ respectively.

To find the probability that at least one student solves the problem, calculate the probability that none of them solve it, then subtract from 1.

The probability each student fails:

Student 1 fails: $1 - \frac{1}{2} = \frac{1}{2}$

Student 2 fails: $1 - \frac{1}{3} = \frac{2}{3}$

Student 3 fails: $1 - \frac{1}{4} = \frac{3}{4}$

Since the students work independently, the probability all three fail:

$P(\text{all fail}) = \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}$

$P(\text{all fail}) = \frac{6}{24}$

$P(\text{all fail}) = \frac{1}{4}$

The probability at least one student solves the problem:

$P(\text{problem solved}) = 1 - P(\text{all fail})$

$P(\text{problem solved}) = 1 - \frac{1}{4}$

$P(\text{problem solved}) = \frac{3}{4}$

Therefore, the probability that the problem is solved is $\frac{3}{4}$ .

2026: 19 May Shift 1

Two cards are drawn successively with replacement from a well shuffled pack of 52 playing cards. Which of the following is correct probability distribution of number of Queens(X) as $\binom{X}{P(X)}$ ?

2022: 6 Aug Shift 2

There are three identical boxes I, II and III, each containing two balls. In box I, both balls are red, In box II, both balls are blue and box III contains one blue ball and one red ball. A boy randomly chooses a box and takes out a ball at random from it. If the ball is red, then the probability that the other ball in the box is also red colour is:

2022: 6 Aug Shift 2

The value of $k$ is

2025: 15 May Shift 1

Match List-I with List-II

if $P(A) = \frac{3}{7}$ , $P(B) = \frac{4}{7}$ and $P(A \cup B) = \frac{5}{7}$

List-I	List-II
(A) $P(A \cap B)$	(I) $\dfrac{2}{3}$
(B) $P(A \mid B)$	(II) $\dfrac{5}{7}$
(C) $P(B \mid A)$	(III) $\dfrac{1}{2}$
(D) $P(A' \cup B')$	(IV) $\dfrac{2}{7}$

Choose the correct answer from the options given below:

2025: 22 May Shift 1

Probability that a man speaks truth is $\frac{3}{4}$ . He throws a die and reports that it is a six. The probability that it is actually a six is

2025: 21 May Shift 2

If two dice are rolled 12 times and getting a total greater than 4 is considered as a success, then which of the following statements are correct?

(A) The probability of getting a total greater than 4 in a single throw of the pair of dice is 5/6.

(B) Mean = 10

(D) The probability of getting a total less than or equal to 4 in a single throw of the pair of dice is 1/6.

Choose the correct answer from the options given below:

A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem is solved is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)