jmc

Question

Rodney uses the following clues to try to guess a secret number: array c It is a two-digit integer. The tens digit is odd. The units digit is even. The number is greater than 65. arrayIf Rodney guesses a number that has each of these properties, what is the probability that Rodney will guess the correct number? Express your answer as a common fraction.

Accepted Answer

We need to count the number of two-digit integers with odd tens digit and even units digit that are greater than

65.

Notice that the only two possibilities for the tens digit are

7

and

9.

For each of these, the units digits

0,

2,

4,

6,

and

8

are all possible, for a total of

5

choices. Therefore there are

2 \cdot 5 = 10

possible integers to choose from. Since there are

10

integers to choose from, the probability of selecting the right one is

\frac{1}{10} .

For your information, the possible numbers are

{70, 72, 74, 76, 78, 90, 92, 94, 96, 98} .