Answer:
30/31 or approximately 0.9677 (rounded to four decimal places).
Explanation:
There are 31 days in the month of August, and we need to determine the probability of selecting a prime number or a double-digit number.
Prime numbers less than 31 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Therefore, there are 10 prime numbers less than 31.
Double-digit numbers less than 31 are: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.
Therefore, there are 21 double-digit numbers less than 31.
However, we need to make sure that we don't count the number 1 as a prime number.
Therefore, the total number of favorable outcomes (prime numbers or double-digit numbers) is 10 + 21 - 1 = 30.The total number of possible outcomes is 31 (since there are 31 days in August).
Thus, the probability of selecting a prime number or a double-digit number in August is 30/31 or approximately 0.9677 (rounded to four decimal places).