Question

Annie and Xenas each arrive at a party at a random time between 2:00 and 4:00. Each stays for 45 minutes and then leaves. What is the probability that Annie and Xenas see each other at the party?

Answer 1

Answer:

P(meet) = 55/64

P(meet) = 0.8594

P(meet) = 85.94%

Therefore, there is a 85.94% probability that Annie and Xenas see each other at the party.

Step-by-step explanation:

Let A denote Annie and X denotes Xenas.

The total time is 2 hours (2:00 to 4:00)

Both A and X stays for 45 minutes or 3/4 hours

The probability that A and X do not meet is given by

P(Not meet) = (3/4)/2 × (3/4)/2

P(Not meet) = 9/64

So the probability that A and X will meet is given by

P(meet) = 1 - P(Not meet)

P(meet) = 1 - 9/64

P(meet) = 55/64

P(meet) = 0.8594

P(meet) = 85.94%

Therefore, there is a 85.94% probability that Annie and Xenas see each other at the party.