Question 15 If E and F are events such that P(E) =, P(F) = and P(E and F) =, find:(i) P(E or F), (ii) P(not E and not F).
Class X1 - Maths -Probability Page 405
Answers
Answered by
0
Given,
P( not E or not F ) = 0.25
P( E' ∪ F' ) =P( E ∩ F)' = 0.25
[ ∵ DeMorgan's law, E' ∪ F' = (E ∩ F)' ]
∴ P( E ∩ F)' = 1 - P(E ∩ F)
⇒0.25 = 1 - P(E ∩ F )
P( E ∩ F) = 1 - 0.25 = 0.75 ≠ 0
Hence, E and F are not mutually exclusive .
[ Note : - Two events A and B are called mutually exclusive , if the occurrence of any one of them excludes the occurrence of the other events . e.g , if they can't occur simultaneously , in this case, the set A and B are disjoint .
For example A = { 1, 2, 3 } and B = { 4, 5, 6 } Then , A ∩ B = Φ = mutually exclusive]
P( not E or not F ) = 0.25
P( E' ∪ F' ) =P( E ∩ F)' = 0.25
[ ∵ DeMorgan's law, E' ∪ F' = (E ∩ F)' ]
∴ P( E ∩ F)' = 1 - P(E ∩ F)
⇒0.25 = 1 - P(E ∩ F )
P( E ∩ F) = 1 - 0.25 = 0.75 ≠ 0
Hence, E and F are not mutually exclusive .
[ Note : - Two events A and B are called mutually exclusive , if the occurrence of any one of them excludes the occurrence of the other events . e.g , if they can't occur simultaneously , in this case, the set A and B are disjoint .
For example A = { 1, 2, 3 } and B = { 4, 5, 6 } Then , A ∩ B = Φ = mutually exclusive]
Similar questions