There are 6 methods of travel (walk,run,unicycle,bicycle,scooter,car).
For three days, Max decides that he wants to randomly select his method of travel taking him to work.
What is the probability that exactly one of the three days, Max walks to work?
there are 6^3 ways to travel on the three days
walking on one day leaves 5^2 options for the other two
p = (3 * 5^2) / (6^3)
Thanks a lot Scott!!
Note that this is also 3(1/6)(5/6)^2
To find the probability that exactly one of the three days Max walks to work, we need to calculate the number of favorable outcomes (where Max walks to work on exactly one day) and the total number of possible outcomes.
Total number of possible outcomes:
Since Max can choose any method of travel from the given 6 methods for each of the 3 days, the total number of possible outcomes can be calculated as:
Total number of possible outcomes = 6 options * 6 options * 6 options = 6^3 = 216
Number of favorable outcomes:
To find the number of favorable outcomes, we need to calculate the number of different ways Max can walk to work on exactly one day.
Max can walk on the first day, second day, or third day. Let's consider each case separately:
Case 1: Max walks on the first day and doesn't walk on the second or third day.
Since Max can choose any of the 6 methods of travel for the first day but cannot choose to walk for the second and third days, the number of ways for this case is:
Number of ways = 1 option * 5 options * 5 options = 25
Case 2: Max doesn't walk on the first day, walks on the second day, and doesn't walk on the third day.
Since Max cannot choose to walk for the first day and the third day, but can only choose to walk on the second day, the number of ways for this case is:
Number of ways = 5 options * 1 option * 5 options = 25
Case 3: Max doesn't walk on the first day, doesn't walk on the second day, and walks on the third day.
Since Max cannot choose to walk for the first and second days, but can only choose to walk on the third day, the number of ways for this case is:
Number of ways = 5 options * 5 options * 1 option = 25
Total number of favorable outcomes:
To find the total number of favorable outcomes, we need to sum up the number of favorable outcomes from each case:
Total number of favorable outcomes = Number of favorable outcomes (Case 1) + Number of favorable outcomes (Case 2) + Number of favorable outcomes (Case 3) = 25 + 25 + 25 = 75
Now we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes = 75 / 216 ≈ 0.3472
Therefore, the probability that exactly one of the three days Max walks to work is approximately 0.3472 or 34.72%.