You know that P (A|B) = P(B|A) and at the same time P(A)+P(B) > 1.Which of the following statements about the events A and B is necessarily true?

agrarismoN07

agrarismoN07

Answered question

2022-11-23

You know that P ( A | B ) = P ( B | A ) and at the same time P ( A ) + P ( B ) > 1.Which of the following statements about the events A and B is necessarilytrue?
a)A and B are exhaustive.
b)A and B are independent.
c) A and B form a partition.
d) A and B are mutually exclusive.
e) None of the above.

Answer & Explanation

driwant9HB

driwant9HB

Beginner2022-11-24Added 11 answers

Consider a dice and the following events:
A: the dice returns an even number ( P ( A ) = 3 6 )
B: the dice returns a number different from 6 ( P ( B ) = 5 6 )
Then P ( A ) + P ( B ) = 8 6 > 1
Hope this can help you to understand that there are cases for which P(A)+P(B)>1. This is because A and B overlaps (A is satisfied for 2,4 and 6, while B is satisfied for 1,2,3,4 and 5). Notice that overlapping does not always means that P ( A ) + P ( B ) > 1 (take B as "the dice returns 1 or 2").
Anyway, if P ( A ) + P ( B ) > 1, you are sure that A and B overlap
Amina Wilkinson

Amina Wilkinson

Beginner2022-11-25Added 2 answers

P ( A ) + P ( B ) P ( A B ) = P ( A B )
So if events A and B overlap, it is possible for P ( A ) + P ( B ) > 1

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