Condtional Probability, Multiplication Rule: random voters

[peggyskold]

I know the events here are independent (or at least I think they are).
I am just not sure on how to determine what numbers to plug in?
In a state where 36% of all voters are Republicans, If two voters are randomly selected for a telephone survery, find the probability that they are both Democrats.

If 36% are Repub. that means that 64% are democrats so would event (A) be 64% and event (B) be 2 out of 64%? I don't think so? I do not know how to determine what the numbers of the events are because I am not sure what the events are. The rule would be p(A) p(B) but how do I determine what the events are? Is this asking what is the probability that 2 out of 64% would be Democrat? Confused?

I think I understand how to do this when the I can more easily identify the events like in this case
You are dealt 2 cards successively without replacing the cards from a deck of 52 cards.
So the events would be dependent and the rule is P(A) P(A/B), so.
4/52 x 3/51 = 12/2652 = 1/221 = 4.525
I think?

Anyone who could help me with this I would appreciate it greatly. Thanks

 

[Deleted member 4993]

Re: Condtional Probability and the Multiplication Rule

I know the events here are independent (or at least I think they are).
I am just not sure on how to determine what numbers to plug in?
In a state where 36% of all voters are Republicans, If two voters are randomly selected for a telephone survery, find the probability that they are both Democrats.

If 36% are Repub. that means that 64% are democrats so would event (A) be 64% and event (B) be 2 out of 64%? I don't think so? I do not know how to determine what the numbers of the events are because I am not sure what the events are. The rule would be p(A) p(B) but how do I determine what the events are? Is this asking what is the probability that 2 out of 64% would be Democrat? Confused?

I think I understand how to do this when the I can more easily identify the events like in this case
You are dealt 2 cards successively without replacing the cards from a deck of 52 cards.
So the events would be dependent and the rule is P(A) P(A/B), so.
4/52 x 3/51 = 12/2652 = 1/221 = 4.525
I think?

Anyone who could help me with this I would appreciate it greatly. Thanks

In this case, the events are independent - because you are choosing from large pool, where pooling out one participant does not affect the probability.

So, (assuming the pool has only Democrats or Republican and every body is either democrat or republican)

Event A - choose one democrat from the pool - what is the probability - 0.64

Event A - choose another democrat from the pool - what is the probability - 0.64

then probablity of event (A) and event (B) (independaent events) happening together = 0.64 * 0.64 = 0.41