Question

determining probability of compound events
a locker combination contains four digits. each digit can be from 0 through 9. what is the probability that a 4 - digit combination chosen at random is made up of 4 digits that are all greater than 6 if each digit can be repeated?

1. find the total number of possible outcomes.
2. (10)(10)(10)(10)
3. find the number of favorable outcomes.
4. (3)(3)(3)(3)
5. use the formula

p (event) = \frac{number of favorable outcomes}{number of possible outcomes}
81/10,000
1/81
1/4
10/625

Explanation:

Step1: Calculate total outcomes

Each digit has 10 choices (0 - 9), so total outcomes = $10\times10\times10\times10=10000$.

Step2: Calculate favorable outcomes

Digits greater than 6 are 7, 8, 9 (3 choices). So favorable outcomes = $3\times3\times3\times3 = 81$.

Step3: Calculate probability

Using the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$, we get $P=\frac{81}{10000}$.

Answer:

81/10,000