saurabh99 wrote:
ARUNPLDb wrote:
The probability that a woman is picked from room A is 10/13
the probability that a woman is picked from room B is 4/9.
Because we are calculating the probability of picking a woman from room A AND then from room B, we need to multiply these two probabilities:
10/13 x 4/9 = 40/117
The probability that a man is picked from room A is 3/13. If that man is then added to room B, this means that there are 3 women and 6 men in room B. So, the probability that a woman is picked from room B is 3/9.
Again, we multiply thse two probabilities:
3/13 x 3/9 = 9/117
To find the total probability that a woman will be picked from room B, we need to take both scenarios into account. In other words, we need to consider the probability of picking a woman and a woman OR a man and a woman. In probabilities, OR means addition. If we add the two probabilities, we get:
40/117 + 9/117 = 49/117
The correct answer is B.
Why do we need to multiply with the probabilities of woman/man picked from room A. After a person is moved from A to B, we will have either 3 women or 4 women.
So why not just add 3/9 + 4/9?? Why to bother about the probability of picking a person from A??
Thanks,
Saurabh
Hi Saurabh,
Picking a member from room B is a dependant event.
What is it dependant on ? As the question reads out " one person is picked from room A AND moved to room B. If a single person is THEN to be picked from B"--> Here FIRST a person is moved THEN picked. So whenever you see such a dependancy , you need to first figure the number of ways of doing the first action.
Whats the first event/action ? Picking and moving a person from room A.
What are our options for event 1 ?Either a man or a woman will be picked.
Hence P(W)= 10/13 or P(M) = 3/13
Now why do we multiply ?Lets say from point A to B there are 2 ways & from point B to C there are 2 more ways ( No direct route from A to C). How many ways do you have from A to C ?
Total number of ways from A to C= ( # of way from A to B ) * (# of ways from B to C)
= 2*2
=4
Coming back to the original question:Case 1: A woman was picked from room A and a woman was picked from room BP(W from room A|| W from room B)= (10/13) * (4/9)
Case 2: A man was picked from room A and a woman was picked from room BP(M from room A|| W from room B)= (3/13) * (3/9)
Total probability: case 1 + case 2 ( This is an or case wherein you add the probabilities)
= (40/117) + (1/13)
= 49/117
Regards,
Shradha