Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Determinants

Question:

For two events A, B

$P(A ∪ B) = \frac{7}{12}, P(A) = \frac{5}{12}, P(B) = \frac{3}{12}$ Then P(A ∩ B) = 

Options:

$\frac{1}{2}$

$\frac{1}{12}$

$\frac{1}{6}$

$\frac{1}{3}$

Correct Answer:

$\frac{1}{12}$

Explanation:

$P(A ∪ B) = \frac{7}{12}, P(A) = \frac{5}{12}, P(B) = \frac{3}{12}$

so P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

= $\frac{3}{12} + \frac{5}{12} - \frac{7}{12}$

= $\frac{1}{12}$