GMAT Practice Question: Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the...
Question
Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member of the crew is to be chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?
- 0
- \frac{1}{10}
- \frac{1}{7}
- \frac{1}{4}
- \frac{1}{3}
Topics: word problems, probability, sets & groups
Solution
Step 1
We name variables for each group and the total crew.
M = 17 B = 18 I = 15 T = 20
Step 2
We use the inclusion–exclusion principle to find how many can use at least one machine.
M + B - I = 17 + 18 - 15 = 20
Step 3
We subtract those who can use at least one machine from the total to find those who cannot use either.
T - 20 = 0
Step 4
We calculate the probability by dividing the number who cannot use either machine by the total crew.
\frac{0}{T} = 0
Answer
0
