South African Mathematics Olympiad

Question

Eskom announces that there is a 60% chance of Stage 1 load shedding for a specific week. In a specific suburb Stage 1 load shedding is from 10:00 to 12:30 on a Monday, Wednesday, Friday and Sunday. What is the probability that in that specific suburb there will be load shedding at a moment in the week, without knowing the day, or time or whether or not it is day or night?

Accepted Answer

There are 7 24 = 168 hours in a week and there are 4 2.5 = 10 hours during which load shedding may occur. Since there is a 60% chance of load shedding, the probability that there is load shedding at a particular moment during the week is 4 2.57 24 60% = 10168 60100 = 128.