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 :slight_smile: 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?

:slight_smile: 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… :slight_smile: