Question

3. A family of 6 is visiting a mall. The mall has 10 exit doors. Assume random selection. Find the probability that a. No family member chooses the same exit door. b. Every family member chooses the same exit door

Answer 1

(A) 0.6

(B) 0.1

Explanation:

(A) Find the probability that NO family member chooses the same exit door.

Now, if no family member chooses the same exit door with another, it means that each person chooses a separate door. If each person chooses a separate door, then 6 out of 10 doors are chosen!

This translates to 6/10 which is = 0.6

So the probability that each family member has a door to him or herself is 0.6

(B) Find the probability that EVERY family member chooses the same exit door.

In this case, the number of persons (family members) does not really count. The focal point of the question is that everybody chooses the same door (and will use the same door). This means that only 1 door out of 10, will be chosen AND the probability that only one door out of 10 will be chosen is

1/10 = 0.1