edited by
11,614 views
42 votes
42 votes

Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are

  1. $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$
  2. $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$
  3. $\left(\dfrac{1}{2}\right),{1}$
  4.   ${1},\left(\dfrac{1}{2}\right)$
edited by

10 Answers

3 votes
3 votes

think like OSA:

Probability of A=1.

Probability of B=1/2


Probability of A given that B has happened, P(A|B)= 1
it has to be one. BECAUSE. Probability of A is 1
and It will still be 1 even if B has happened(unless B reduces it)
Since A and B(intersection) is non zero.

SO only option D is right!

3 votes
3 votes
Here P(A) and P(B) are given :

So, P(A) = 1 and P(B) = ½

We have to find P(A|B) and P(B|A)

We know that P(A|B) = P(A∩B)/P(B) similarly P(B∩A)/P(A)

So we know that P(A∩B) = P(A) * P(B) = 1*½ = ½

So put this in the above formula:

P(A|B) = ½/½ = 1

P(B|A) = ½/1 = ½

So the final answer is 1 and (1/2) respectively.

Option – (D)
1 votes
1 votes
First of all the divison must be half because p(A/B) / p(B/A)=1 . 1/2 so the answer must be option c or option d ..now p(A/B) is always 1 as the p(A)=1 and it doesnt depend any other event so option d is correct
1 votes
1 votes

An analogy that may help to relate with the question :

Say we are living in an area where it rains everyday (Event A) and there are two groups of day MWF and TTS (Just assume that Sunday doesn't exist at all). Let Event B be that the chosen day is one amongst MWF. Clearly the event A has probability of 1 and probability of event B is 1/2.

Now the question can be interpreted as : 

P(A|B) = Given that the day chosen is among MWF, probability of raining ?

Since it is raining no matter what, therefore the probability of this part is 1.

P(B|A) = Given that it is raining, probability that the day is one of MWF ?

Since it rains on all days, the probability that the randomly chosen day is one amongst MWF is 3/6 or 1/2.

Answer:

Related questions

42 votes
42 votes
5 answers
1
Kathleen asked Sep 17, 2014
9,040 views
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ respectively denote the probability density functions of time taken to execute the two ...
27 votes
27 votes
4 answers
2
go_editor asked Sep 29, 2014
8,368 views
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?$\left(\dfrac{1}{3}\right)$$\le...