Probability Question

[PassOrNothing]

If someone could clarify my misunderstanding in probability question below, that would be much appreciated.

Q) The joint probability of events A & B is 32% with the P(A) = 60% and P(B) = 50%. Based on this info, the conditional probability of event A given B has occured is

A) 64%

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My questions:

1. I set the problem as P(A | B) , which equals P (A*B) / P (B). I memorized that formula but what’s the logical idea behind this?

2. The question states that the joint prob of A &B is 32%. But doesn’t this mean P(A * B) which is P (A) * P (B), which can be recalculated by .6 * .5 = 30%? why is there a 2% difference?

[S2000magician]

@PassOrNothing

If someone could clarify my misunderstanding in probability question below, that would be much appreciated.

Q) The joint probability of events A & B is 32% with the P(A) = 60% and P(B) = 50%. Based on this info, the conditional probability of event A given B has occured is

A) 64%

–

My questions:

1. I set the problem as P(A | B) , which equals P (A*B) / P (B). I memorized that formula but what’s the logical idea behind this?

I’m not sure what you mean by P(A*B); I hope that you mean P(A&B), normally written as P(AB).

In any case:

P(AB) = P(A|B)P(B)

Divide both sides by P(B).

@PassOrNothing

2. The question states that the joint prob of A &B is 32%. But doesn’t this mean P(A * B) which is P (A) * P (B), which can be recalculated by .6 * .5 = 30%? why is there a 2% difference?

P(AB) = P(A) × P(B) only when A and B are independent. Here, obviously, they’re not.

[PassOrNothing]

perfect explanation, thanks!!

[S2000magician]

@PassOrNothing

perfect explanation . . .

That happens sometimes, despite my usual efforts.

@PassOrNothing

. . . thanks!!

My pleasure.

[BaseballRedhawks]

So what is the calculation to get the answer? Im so terrible at all of these P(AB), probability stuff…

[PassOrNothing]

It is 64%.

= .32 / .50