Question

Nick randomly selects a digit from the set {0, 1, 2, ..., 9} and a letter from the set {A, B, C, ..., Z}. Matthew will try to guess both the digit and the letter. Which expression gives the probability that Matthew will incorrectly guess both the digit and the letter?"

1. (9/10) * (25/26)
2. (1/10) * (1/26)
3. (9/10) * (1/26)
(4. 1/10) * (25/26)

Answer 1

The probability that Matthew will incorrectly guess both the digit and the letter is calculated by multiplying the probabilities of incorrectly guessing the digit and the letter, which is (9/10) * (25/26).

Step-by-step explanation:

The question is asking for the probability that Matthew will incorrectly guess both the digit and the letter. To find this, we calculate the probability of failing to guess each correctly and then multiply those probabilities because the events are independent.

There are 10 possible digits (0-9) and 26 possible letters (A-Z). If the digit is selected randomly, the probability that Matthew guesses the digit incorrectly is 9 out of 10 possibilities, since there is only one correct digit and nine incorrect ones. This is (9/10).

Similarly, the probability that Matthew guesses the letter incorrectly is 25 out of 26 possibilities, which is (25/26). So, the probability that he incorrectly guesses both the digit and the letter is the product of these two probabilities: (9/10) * (25/26).