A small combination lock on a suitcase has 4 wheels, each labeled with the digits from 0 to 9. If an opening combination is a particular sequence of 4 digits with no repeats, what is the probability of a person guessing the right combination?
To find the probability of guessing the right combination, we need to determine the total number of possible combinations and divide it by the total number of outcomes.
In this case, the total number of possible combinations can be calculated using the permutation formula, nPr, where n is the total number of choices and r is the number of choices made.
In a combination lock with 4 wheels, each labeled with the digits 0 to 9, there are 10 choices for each wheel (0-9). Since there are no repeats allowed, the number of choices decreases by 1 for each subsequent wheel. Therefore, the total number of possible combinations can be calculated as:
10 * 9 * 8 * 7 = 5,040
Next, we need to determine the total number of outcomes. Since there are 10 digits (0-9) on each wheel, the total number of outcomes for each wheel is 10.
Therefore, the total number of outcomes can be calculated as:
10 * 10 * 10 * 10 = 10,000
Finally, we can calculate the probability by dividing the total number of possible combinations by the total number of outcomes:
P(guessing the right combination) = 5,040 / 10,000 = 0.504
So, the probability of guessing the right combination on the small combination lock is approximately 0.504, or 50.4%.
10*9*8*7 possible combinations
only 1 works, so ...