# Joint Probabilty

Please explain: Thanks S A joint probability of A and B must always be: A) greater than or equal to the conditional probability of A given B. B) less than or equal to the conditional probability of A given B. C) greater than or equal to than the probability of A or B. D) less than the probability of A and the probability of B.

P(A | B ) = P (A and B) / P(B) so which is bigger?

Considering that: P(A and B)= P(A | B) x P (B) Joint probability = Conditional probability x Probability (b) or P(A|B)= P (A and B)/ P(B) There is a high probability than the result is B.

Bonus question: When is it less than and when is it equal to the conditional probability of A given B?

If P(B)=1 then P(A and B) will be equal to P(A|B) Less then… I think never

Given, P(A | B ) = P (A and B) / P(B) , but P(B) can only be within 0 and 1, except for when P(B) = 1, therefore P(A and B) > P(A|B) answer is A

So when does that happen? When does P(B) =1? Under what condiitons does it become “less than”?

Grimer, no.

Dreary do you agree with my previous answer? Suggestion are welcome

What is wrong with D? S

> Less then… I think never Not true.

P (A) + P(B) = P(A or B) + P(A and B) or P (A) + P(B)= P (A or B) + P(A)xP(A|B) [P(A) + P(B)] - P (A or B) = P (A and B) Therefore the joint probability of P(A and B) cannot never be less than P(A) + P(B)

strangedays Wrote: ------------------------------------------------------- > P (A) + P(B) = P(A or B) + P(A and B) > > or > > P (A) + P(B)= P (A or B) + P(A)xP(A|B) > > - P (A or B) = P (A and B) > > Therefore the joint probability of P(A and B) > cannot never be less than P(A) + P(B) Sorry… I meant that the joint probability of P(A and B) > is never less than P(A) + P(B)

I wannna hear someone else try this…it’s rather easy. Hint: P(Sunny in China) = 0.40 P(Sunny in France) = 0.60

P (A) + P(B) = P(A or B) + P(A and B) P (sunny in china) + P ( sunny in France) = P (sunny in China or France) + P (sunny in China and France). 0.4 + 0.6 = (0.4 + 0.6 ) - P (sunny in China and France) + P (sunny in China and France). Therefore if two event are mutually exclusive P (A) + P (B) = P(A or B) plus I have a 0.6 probability that you are french P (A) + P(B)= P (A or B) + P(A)xP(A|B) - P (A or B) = P (A and B)

Conditional probability = joint probability / marginal probability Joint is always less than or equal to conditional.

Wow, how do you edit?

So Dreary…tell us which one do you think its the correct answer

wyantjs, Under what condiitons does it become “less than”? Under what condiitons does it become equal?

Olala… Dreary now I am 100% sure you are french…