Arjun hits a target with probability 2/3 and Nandini hits it with probability 3/5. Each fires one shot, independently of the other. What is the probability that both of them hit the target?

Question 39

MediumOriginal question

Arjun hits a target with probability $\frac{2}{3}$ and Nandini hits it with probability $\frac{3}{5}$ . Each fires one shot, independently of the other. What is the probability that both of them hit the target?

\frac{2}{15}

Correct answerYour answer

\frac{4}{15}

Correct answerYour answer

\frac{13}{15}

Correct answerYour answer

\frac{2}{5}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

For independent events, P(both) = product of the probabilities.
P(both hit) $= \frac{2}{3} \times \frac{3}{5} = \frac{6}{15} = \frac{2}{5}$ .

Worth noting

$\frac{2}{15}$ is the chance that both MISS $\left(\frac{1}{3} \times \frac{2}{5}\right)$ , and $\frac{13}{15}$ is the chance that at least one hits. $\frac{4}{15}$ is P(Arjun hits and Nandini misses).

Concept: Multiplying probabilities of independent events
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsBasic probability

Practise this chapter →

Ten questions from Counting and Basic Probability, at your own pace.

Arjun hits a target with probability 23\frac{2}{3}32​ and Nandini hits it with probability 35\frac{3}{5}53​. Each fires one shot, independently of the other. What is the probability that both of them hit the target?

Explanation

Arjun hits a target with probability $\frac{2}{3}$ and Nandini hits it with probability $\frac{3}{5}$ . Each fires one shot, independently of the other. What is the probability that both of them hit the target?