Algebra

Probability

Medium

core

The probability that A hits a target is $\frac{1}{5}$ and the probability that B hits it is $\frac{2}{3}$ . The probability that the target will be hit if both A and B shoot at it independently is:

$\frac{11}{15}$

$\frac{1}{15}$

$\frac{2}{15}$

$\frac{4}{15}$

✅ Correct Option: 1

We need to find the probability that the target is hit, meaning at least one of A or B hits it.

$P(A \text{ hits}) = \dfrac{1}{5}$

$P(B \text{ hits}) = \dfrac{2}{3}$

Instead of calculating each case separately (only A hits, only B hits, both hit), we use a faster approach:

$P(\text{at least one hits}) = 1 - P(\text{nobody hits})$

$P(A \text{ misses}) = 1 - \dfrac{1}{5} = \dfrac{4}{5}$

$P(B \text{ misses}) = 1 - \dfrac{2}{3} = \dfrac{1}{3}$

Since A and B shoot independently, we can multiply their miss probabilities to get the probability that both miss:

$P(\text{both miss}) = \dfrac{4}{5} \times \dfrac{1}{3} = \dfrac{4}{15}$

Using the complement:

$P(\text{target is hit}) = 1 - \dfrac{4}{15} = \dfrac{15 - 4}{15} = \boxed{\dfrac{11}{15}}$

2025: 15 May Shift 2

A player participates in 3 matches against three teams T₁, T₂ and T₃.The probability of winning a match against teams T₁, T₂ and T₃ are 0.2, 0.3 and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he

(A) wins all the 3 matches is 0.054

(B) wins no match is 0.054

(D) wins exactly one match is 0.542

Choose the correct answer from the options given below:

2026: 22 May Shift 2

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

2022: 30 Aug Shift 1

The probability that task is completed on time by at least one of them is:

2026: 30 May Shift 1

A company manufactured a product through 4 units. A, B, C and D. The probability that a product is manufactured are $\frac{3}{10},\frac{1}{5},\frac{1}{10}$ and $\frac{2}{5}$ by units A, B, C and D respectively. The probability that it will be defective are $\frac{1}{4},\frac{1}{3}$ and $\frac{1}{12}$ if it is produced by A, B, C respectively and there is no defective from unit D. A product is chosen, it is found to be defective.

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. The Probability that the defective product is from A	I. 4/9
B. The Probability that the defective product is from B	II. 0
C. Probability of defective product	III. 1/2
D. Probability that the defective product is from D	IV. 3/20

Choose the correct answer from the options given below:

2026: 30 May Shift 1

Probabilities of solving a specific mathematical problem independently by three students are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ . If all the three students try to solve the problem independently, the probability that the problem is solved, is:

2026: 26 May Shift 2

A random variable $X$ has the following probability distribution:

X	0	1	2	3	4
P(X)	0	$\dfrac{k}{2}$	$\dfrac{3k}{2}$	$\dfrac{k}{3}$	$2k$

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Value of $k$	I.	$\dfrac{7}{13}$
B.	Value of $P(X \leq 3)$	II.	$\dfrac{3}{26}$
C.	Value of $P(X > 1)$	III.	$\dfrac{23}{26}$
D.	Value of $P(X < 2)$	IV.	$\dfrac{3}{13}$

Choose the correct answer from the options given below:

The probability that A hits a target is 15\frac{1}{5}51​ and the probability that B hits it is 23\frac{2}{3}32​. The probability that the target will be hit if both A and B shoot at it independently is:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The probability that A hits a target is $\frac{1}{5}$ and the probability that B hits it is $\frac{2}{3}$ . The probability that the target will be hit if both A and B shoot at it independently is: