Question

A certain 5-digit combination lock can be reset with a new combination. The lock uses numbers from 1 to 6. After a friend accidentally resets it to an unknown combination, what is the probability that you guess the combination that opens the lock? A. 100,000 B. 7,776 C. 1100,000 D. 17,776

Answer 1

Answer:

The correct answer is B. 7776

Step-by-step explanation:

$\text{Probability of selecting one correct choice from available 6 choices= }\frac{1}{6}$

Since the locks combination are independent of each other, you can multiply the probabilities together. There are 6 possible numbers for each lock and there are 5 locks.

$\text{So, Probability of guessing the correct combination = }\frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}\\\\=(\frac{1}{6})^5=\frac{1}{7776}$