6,113 views
35 votes
35 votes
Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 pm and 5:00 pm and will see if the other has already arrived. If not, they will wait for 10 minutes or the end of the hour whichever is earlier and leave. What is the probability that the two will not meet?

4 Answers

Best answer
40 votes
40 votes
We are given that both will be reaching the park between $4:00$ and $5:00$.

Probability that one friend arrives between $4:00$ and $4:50 = \dfrac{5}{6}$
Probability that one friend arrives between $4:00$ and $4:50$ and meets the other arriving in the next $10$ minutes $=\dfrac{5}{6}\times \dfrac{1}{6}\times {2} =\dfrac{10}{36} =\dfrac{5}{18}.$
(For any time of arrival between $4:00$ and $4:50,$ we have a $10$ minute interval possible for the second friend to arrive, and $2$ cases as for choosing which friend arrives first)

Probability that both friend arrives between $4:50$ and $5:00 =\dfrac{1}{6}\times \dfrac{1}{6} =\dfrac{1}{36}.$

This covers all possibility of a meet. So, required probability of non-meet

$=1 - \left( \dfrac{5}{18} + \dfrac{1}{36}\right)$
$= 1 - \dfrac{11}{36}$
$=\dfrac{25}{36}.$
edited by
27 votes
27 votes

we can also solve like this -

7 votes
7 votes

Simple trick 

probability that one person meet on that day = 10/60 = 1/6
Probability(failing to meet) = 1-1/6=5/6
probability(failing to meet by both the persons) = 5/6*5/6= 25/36
Answer:

Related questions

61 votes
61 votes
3 answers
1
Arjun asked Sep 26, 2014
17,270 views
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
30 votes
30 votes
8 answers
2
Kathleen asked Sep 25, 2014
8,428 views
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is$\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}...
24 votes
24 votes
2 answers
4
Arjun asked Feb 12, 2020
12,125 views
For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigm...