Let E and F be events with P(E) = 5 ,P(F) = 10 and P(E F) = 5 . Are E and F independent?

.: P(E) P(F) = 5 10 = 50 5 = P(E F) Therefore, E and F are not independent.

Probability — Class 12 Maths Solution

ncert exercise SA NCERT,EX.13.2,Q.6,Page.546

Question

Let $E$ and $F$ be events with $P(E) = \cfrac{3}{5},P(F) = \cfrac{3}{{10}}$ and $P(E \cap F) = \cfrac{1}{5}.$ Are $E$ and $F$ independent?

Step-by-step Solution

.: $P(E) \times P(F) = \cfrac{3}{5} \times \cfrac{3}{{10}} = \cfrac{9}{{50}} \ne \cfrac{1}{5} = P(E \cap F)$

Therefore, $E$ and $F$ are not independent.

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Probability. Curated by Sachin Sharma. Free for all students.