A medium difficulty GRE Quant Sample Question in Probability.
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
(e) 0.35 ≤ P ≤ 0.6
Answer: (c)
Explanation to GRE Quant Question
Step 1: Compute Minimum Probability
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. Essentially, we are maximizing the number of days she did not work at the office the entire day.
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, for a minimum of 40% of the days she could have worked the entire day.
Step 2: Compute Maximum Probability
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. Essentially, we are minimizing the number of days she did not work at the office the entire day.
i.e., the days she went late to office is a subset of the days she left early from office.
Hence, 35% of the days she would have either gone late of left early from office.
Therefore, for a maximum of 65% of the days she could have worked the entire day.
Step 3: Compute the range
The range of values the probability that she worked the entire day takes values from 0.4 to 0.65
0.4 ≤ P ≤ 0.65
Option C is the correct answer to this GRE Probability Practice Question.