what is the probability?

Question

a NY real estate agent lists two houses for lease in the same street,

one built brick and the other of timber.

the agent estimates that the probability of being leased within one week is 0.96 for the brick and 0.97 for the timber house,
and the probability for both being leased within one week is 0.51


if the timber house is leased within one week, what is the
probability that the brick house is also leased within one week?

Answer 1

Disregard the other answers... they mean well but don't know what they're talking about in this case. This is testing your knowledge of Baye's Rule and conditional probability.

Baye's Rule: P(B|A) = P(B&A)/P(A), which read as: The probability that B occurs gives that A has occured = the probability of both A and B occuring divided by the probability of just A occuring.

In your case:
The chance that the brick house will lease = P(B) = .96
The chance that the wood house will lease = P(W) = .97
The chance that both lease = P(A & B) = .51

So the probability that the brick house will lease given that the wood house leased is : .51/.97 = .525773 ~= .53

Answer 2

i think my argument won't be properly gained. I say the threat is 50% enable a ??, enable b ?? and randomly go with the values for a and b. As already stated, for a ? 0, P( a < b²) = a million, that's trivial. in basic terms slightly much less trivial is the thought P(a < 0 ) = a million/2 and consequently P( a < b² | a ? 0) = a million and P( a < b² ) ? a million/2 Now evaluate what occurs while a > 0 For a > 0, on an analogous time as that's trouble-free to coach there's a non 0 threat for a finite b, the shrink, the threat is 0. a < b² is resembling asserting 0 < a < b², keep in mind we are in basic terms staring at a > 0. If this a finite era on an infinite line. The threat that a is an ingredient of this era is 0. P( a < b² | a > 0) = 0 As such we've a entire threat P( a < b² ) = P( a < b² | a ? 0) * P(a ? 0) + P( a < b² | a > 0) * P(a > 0) = a million * a million/2 + 0 * a million/2 = a million/2 keep in mind, that is through countless contraptions. no rely what variety of era you draw on paper or on a working laptop or computing gadget you will detect a finite threat that looks to physique of ideas a million. yet that's through finite random style turbines on the computing gadget and if we had this query asked with finite values there would be a a answer extra desirable than 50%. i do no longer recommend to be condescending, yet please clarify why making use of the Gaussian to approximate a uniform distribution is a good suggestion? are not countless numbers relaxing. Cantor while mad working with them! :)

Answer 3

As long as the probabilities are independent, 0.96. The fact that the timber house is leased has absolutely no bearing on the brick house, since the timber house's probability is, of course, 1.00.

For you moro... nice people suggesting I'm wrong, consider this:
I have a 10% chance of wearing clown shoes and a 60% chance of getting struck by lightning, and the chance of both occuring is 6%. If we SUPPOSE that I'm wearing clown shoes, you can totally discard that 6%- one element of the probability is already assumed. IF I wear clown shoes, it doesn't reduce my chance of being struck by lightning-- you should be able to rationalize that logically. I shouldn't have to say this, but if I'm wearing clown shoes, the probability that I'm wearing clown shoes is 100%. You don't have to actually do any math: the chance of being hit by lightning is still 60%.

Answer 4

Mathematicians and actuaries think of probabilities as numbers in the closed interval from 0 to 1 assigned to "events" whose occurrence or failure to occur is random. Probabilities P(A) are assigned to events A according to the probability axioms.

The probability that an event A occurs given the known occurrence of an event B is the conditional probability of A given B; its numerical value is (as long as P(B) is nonzero). If the conditional probability of A given B is the same as the ("unconditional") probability of A, then A and B are said to be independent events. That this relation between A and B is symmetric may be seen more readily by realizing that it is the same as saying when A and B are independent events.

Two crucial concepts in the theory of probability are those of a random variable and of the probability distribution of a random variable.

Answer 5

Well, it means that they are both leased within one week, u have given that probability for both being leased within one week is 0.51

Answer 6

they don't change ( if both are leased the first day the original calculation does not change )

Answer 7

Same street houses would not be built of the same material.

Answer 8

uhm i have no idea but it sounds like your trying to get us to do your homework

Answer 9

0.97 * 0.51
= 0.4947

Answer 10

.00000698%