Question

a lock consists of 3 dials, where each dial has 4 letters. what is the probability of guessing the right combination in one try?

Explanation:

Step1: Calculate total combinations

Use the multiplication principle. Each dial has 4 letters. For 3 dials, total combinations = \(4\times4\times4 = 4^{3}=64\)

Step2: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Favorable outcomes = 1 (right combination), total outcomes = 64. So \(P = \frac{1}{64}\)

Answer:

\(\frac{1}{64}\)