Two neighbors,Ann and Becky, illuminate their houses before christmas. They each randomly turn on the lights between 6 pm and midnight. Ann keeps the lights on for 1.5 hrs and Becky for 2.5 hrs

Question

Today both houses were illuminated at some time simultaneously. Find the probability that both houses were illuminated at 10 pm exactly.

Answer 1

A 1.5 hours

B 2.5 hours

6pm to midnight = 6 hours

at 10 pm what is the probability both their lights will be on?

use a Venn diagram. or Bayes Theorem

Universe set is 6, A is 1.5, B=2.5, they overlap at (1.5)(2.5)/6^2 = 3.75/36 = about 10.42%

P(A) = 1.5/6 = 3/12= 1/4

P(B) = 2.5/6 = 5/12

P(A)P(B) = 5/12)(1/4) = 5/48 = about 10.42% chance both have lights on at any time between 6 pm and midnight, including at 10pm