If E and F are events such that P (E) = 1/4, P (F) = 1/2, and (E and F) = 1/8, find 
(i) P (E or F),   (ii) P (not E and not F)

Solution:

Here, P (E) = 1/4, P (F) = 1/2, and P (E and F) = 1/8

(i) Using the addition theorem of probability,

P (E or F) = P (E) + P (F) - P (E and F)

Therefore,

P ( E or F) = 1/4 + 1/2 - 1/8

= (2 + 4 - 1)/8

= 5/8

(ii) From (i), P (E or F) = P (E υ F) = 5/8 ... (1)

By De Morgan’s law,

(E' ∩ F') = (E υ F)'

Therefore,

P (E' ∩ F') = P (E υ F)'

= 1 - P(E υ F)

= 1- 5/8 (From (1))

= 3/8

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 15

If E and F are events such that P (E) = 1/4, P (F) = 1/2, and (E and F) = 1/8, find (i) P (E or F), (ii) P (not E and not F)

Summary:

If E and F are events such that P (E) = 1/4, P (F) = 1/2, and (E and F) = 1/8 then

(i) P(E or F) = 5/8 (ii) P (not E and not F) = 3/8