Question

todd forgot the first two numbers of his locker combination. the numbers can be any number 1 through 8. what is the probability that he will guess the first number correctly and the second number incorrectly? a. \\(\frac{7}{64}\\) b. \\(\frac{1}{16}\\) c. \\(\frac{7}{16}\\) d. \\(\frac{1}{8}\\)

Explanation:

Step1: Probability of correct first guess

There are 6 total numbers (1-6), so the probability of guessing the first number correctly is $\frac{1}{6}$.

Step2: Probability of incorrect second guess

There are 5 wrong numbers out of 6, so the probability of guessing the second number incorrectly is $\frac{5}{6}$.

Step3: Multiply the two probabilities

Since the two events are independent, multiply their probabilities: $\frac{1}{6} \times \frac{5}{6} = \frac{5}{36}$.

Answer:

A. $\frac{5}{36}$