Meera can solve a puzzle with probability 3/4 and Joseph with probability 2/5. They try it independently. What is the probability that the puzzle gets solved, that is, at least one of them solves it?

Question 40

MediumOriginal question

Meera can solve a puzzle with probability $\frac{3}{4}$ and Joseph with probability $\frac{2}{5}$ . They try it independently. What is the probability that the puzzle gets solved, that is, at least one of them solves it?

\frac{3}{20}

Correct answerYour answer

\frac{17}{20}

Correct answerYour answer

\frac{11}{20}

Correct answerYour answer

\frac{3}{10}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The puzzle stays unsolved only if BOTH fail: $\frac{1}{4} \times \frac{3}{5} = \frac{3}{20}$ .
P(solved) $= 1 - \frac{3}{20} = \frac{17}{20}$ .

Worth noting

$\frac{3}{20}$ is the chance it is NOT solved. $\frac{3}{10}$ is P(both solve) and $\frac{11}{20}$ is P(exactly one solves); 'at least one' includes both of those cases.

Concept: 'At least one' through the complement
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsBasic probability

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

Meera can solve a puzzle with probability 34\frac{3}{4}43​ and Joseph with probability 25\frac{2}{5}52​. They try it independently. What is the probability that the puzzle gets solved, that is, at least one of them solves it?

Explanation

Meera can solve a puzzle with probability $\frac{3}{4}$ and Joseph with probability $\frac{2}{5}$ . They try it independently. What is the probability that the puzzle gets solved, that is, at least one of them solves it?