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?

259/260 or 0.99615 (depending on which answer format your teacher wants)

There are 10 numbers in the set {0, 1, 2, ..., 9}. There are 26 letters in the set {A, B, C, ..., Z}. Multiply those values: 10*26 = 260. So there are 260 ways to pick a number followed by a letter. One example is 7P.

There is only one way Matthew can get the correct answer, and there are 260 - 1 = 259 ways to get the wrong answer. We divide 259 over 260 to get the probability of getting the incorrect answer, which is 259/260.

If you need this fraction in decimal form, then use a calculator to find that 259/260 = 0.99615 approximately

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