Bunuel wrote:
Two persons agree to meet at between 2 PM to 4 PM, but each of them will wait 30 minutes for the late comer. What is the probability that they will meet ?
A. 7/8
B. 1/2
C. 7/16
D. 3/8
E. 7/32
Are You Up For the Challenge: 700 Level Questions: 700 Level QuestionsI could not get to the answer. This is what i did later(Assuming the meeting happens exactly at 30 minutes).
The earliest both A and B can meet is 2:30pm when either of A or B arrived at 2:00pm. Let's say A comes first and waits for B to join.
As A can arrive at any minute there are 120(2hr=120min) possibilities for arrivals. However, for last 30minutes(3:30pm to 4:00pm) A can't arrive first, in which case B must have arrived earlier or vice-a-versa.
So, for the time period between 2:30 to 3:30(i.e. 60 minutes), Probability of meeting = \(\frac{60}{120} = \frac{1}{2}\) for both.
Hence Probability of meeting = \(\frac{1}{2}*\frac{1}{2} = \frac{1}{4}\)
Now, from 2:00pm to 2:30pm there is a restriction for the meeting as neither A nor B can come before 30 minutes. So, for the time period 3:30 to 4:30, either of them can come earlier than other, starting at 3:01 to 3:30.
Suppose A comes first, Probability of A meeting B is \(\frac{30}{120} = \frac{1}{4}\)
under the condition that B arrives after A from 3:01 to 3:30pm.
Probability of B meeting A = 30/120 = \(\frac{1}{4}\)
Probability of both A and B meeting = \(\frac{1}{4} * \frac{1}{4} = \frac{1}{16}\)
Required probability = \(\frac{1}{4} + \frac{1}{16} = \frac{5}{16}\)
Looks like i did something wrong.
chetan2u I have gone through your solution but don't understand the latter part. Please help.
Bunuel Please do provide official solution.
Thanks.
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