Events E and F are such that P (not E or not F) = 0.25. State whether E and F are mutually exclusive

Solution:

It is given that; P (not E or not F) = 0.25

i.e., P (E' υ F') = 0.25

By De Morgan’s law,

(E' υ F') = (E ∩ F)'

Therefore,

P (E' υ F') = P (E ∩ F)' = 0.25 ... (1)

We know that E and F are said to be mutually exclusive only when P(E ∩ F) = 0.

Now,

P (E ∩ F) = 1 - P (E ∩ F)'

= 1 - 0.25 (From (1))

= 0.75

≠ 0

Hence,

P (E ∩ F)' ≠ 0

Thus, E and F are NOT mutually exclusive

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NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 16

Events E and F are such that P (not E or not F) = 0.25. State whether E and F are mutually exclusive.

Summary:

If events E and F are such that P (not E or not F) = 0.25, then E and F are NOT mutually exclusive