Question

You and your partner each arrive at a coffee shop at some random time (uniformly distributed)
between 1 pm and 3 pm. Both of you stay exactly 1 minutes and then leave.
(a) What is the probability that you will meet on a given day?
(b) Estimate the probability that the number of days you meet in the year of 2020 is larger
than 4 as a decimal. Use an approximation technique, rather than calculating the exact
probability

Answer 1

a.

P(meet) = P(second person comes within next 1 min)

= (1) / (minutes between 1 pm and 3pm)

= 1 / 120

= 0.0083

b.

mean no. of days = n*p = 365*0.0083 = 3.0295

SD = [n*p*(1-p)]^0.5 = [365*0.0083*(1-0.0083)]^0.5

= 1.7333

for no. of days > 4

we use > 4.5 (as no. of days is discrete while in aprroximation we take conitnuous)

ANSWER : 0.1981

(please UPVOTE)