Problem solving - probability max,min


Ms Li works at an office where the work timing is from 9:00 AM to 6:00 PM. 25% of a year she goes late to office and 35% of a year she leaves early from office. If P is the probability that she works at office the entire day then

(a) 0.25 <= P <= 0.35
(b) 0.25 <= P <= 0.65
(c) 0.4 <= P <= 0.65
(d) 0.35 <= P <= 0.4

Answer: (c)

Explanation:

The minimum value for the probability P is obtained by considering that on none of the days when she went late to office did she leave early from office. This means that (25% + 35%) = 60% of the days she either went late to office or left early from office i.e.,  60% of the days she did not work the entire day. Hence 40% of the days she could have worked the entire day.

Next, to establish the maximum value for the probability P, consider that 25% of the days when she went late to office falls under the 35% of days when she left early from office. Hence 35% of the days she would have either gone late of left early from office. Hence, 65% of the days she could have worked the entire day.