Question

(a) Given E and F are events defined on a sample space S such that P(E)=0.3, P(F)=0.5 and find the probability of occurrence of,
(i) Either event E or event F or both
(ii) Event E but not event F.
(iii) Event F but not event E.
(iv) Neither event E nor event F

Answer 1

Answer:

Either event E or event F or both

Answer 2

Given : Given E and F are events defined on a sample space S such that P(E)=0.3, P(F)=0.5  

To find :  the probability of occurrence of,

(i) Either event E or event F or both

(ii) Event E but not event F.

(iii) Event F but not event E.

(iv) Neither event E nor event F

Solution:

Assuming E and F are independent event

P(E)=0.3,  P(F)=0.5  

P ( E ∩ F ) = P(E). P(F) = 0.3 * 0.5 = 0.15

(i) Either event E or event F or both

=> P ( E ∪ F)  =  P(E) + P(F)  - P ( E ∩ F )

=>  P ( E ∪ F)  = 0.3 + 0.5 -  0.15

=>  P ( E ∪ F)  = 0.65

Event E but not event F

=>  P(E) - P ( E ∩ F )   =  0.3 - 0.15  = 0.15

Event F but not event E.

=>  P(F) - P ( E ∩ F )   =  0.5 - 0.15  = 0.35

Neither event E nor event F

P(not E) . P(not F)  =  (  1 - P(E) )(1 - P(F))

=  0.7 * 0.5

= 0.35

or

Neither event E nor event F    1 - P ( E ∪ F) = 1  - 0.65 = 0.35

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