Probability

rajan_agarwal wrote:Q. A and B are suppose to meet between 5-6 pm, A and B will wait for 20 mins whoever reaches first, find out the probability that they will meet.

ans:1/3

I'm sure that the prompt stipulates that A and B are each equally (and independently) likely to arrive at ANY time from 5:00 to 6:00. Assuming that, we could solve the problem as follows. (If you haven't done any geometric probability before, here's a good introduction.)

A and B will arrive in the same 20 minute interval in the red band in the square shown. To find the probability, we only need to find the ratio of the area of the red band to the area of the square.

The two triangles (in which A and B do NOT meet) each have sides that are (2/3) the side of the square. So if the square has area 1, the triangles each have area (2/3)*(2/3)/2, or 2/9.

So the area of the red band = 1 - 2/9 - 2/9, or 5/9, and the probability that the two friends meet is 5/9.

Matt@VeritasPrep wrote:I'm sure that the prompt stipulates that A and B are each equally (and independently) likely to arrive at ANY time from 5:00 to 6:00. Assuming that, we could solve the problem as follows. (If you haven't done any geometric probability before, here's a good introduction.)

A and B will arrive in the same 20 minute interval in the red band in the square shown. To find the probability, we only need to find the ratio of the area of the red band to the area of the square.

The two triangles (in which A and B do NOT meet) each have sides that are (2/3) the side of the square. So if the square has area 1, the triangles each have area (2/3)*(2/3)/2, or 2/9.

So the area of the red band = 1 - 2/9 - 2/9, or 5/9, and the probability that the two friends meet is 5/9.

Hey Matt,

Thanks for the explanation, but the triangles seem to be 3/4 of the side of the square right? ( From 6 to 5:20). What am I doing wrong?

Thanks

EDIT: sorry i seem to be blind and/or retarded, now I see it, thanks