Question

Probablity Question

Answer 1

Check whether the following probabilities P(A) and P(B) are consistently defined
(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8

Answer 2

i found an answer here but it doesn't making sense to me

http://www.meritnation.com/ask-answer/question/check-whether-the-following-probabilities-p-a-and-p-b-are/probability/6322947

Answer 3

in order to be consistently defined:

P(A ∩ B) must be less than or equal to P(A) and P(B)
P(A ∪ B) must be greater than or equal to P(A) and P(B)

Answer 4

u mean both conditions or any one condition should be satisfied

Answer 5

both

Answer 6

so, for the first one (i) what do you think the answer is?

(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6

Answer 7

consistentlyt defined

Answer 8

not quite, check the first condition again...

P(A ∩ B) must be less than or equal to P(A) and P(B)

Answer 9

notice how P(A ∩ B) is greater than P(B)?

Answer 10

these

"P(A ∩ B) must be less than or equal to P(A) and P(B)
P(A ∪ B) must be greater than or equal to P(A) and P(B)"

are necessary conditions but not sufficient

Answer 11

i am confused

Answer 12

The second one is possible, since they can overlap 0.2 to get A U B = 0.8