Final answer:
To find the probability of selecting a prime number less than 50 at random, count the prime numbers in this range (there are 15) and divide by 49 (the total numbers considered). The probability is about 0.306 when rounded to three decimal places.
Step-by-step explanation:
The question asks for the probability that a positive integer less than 50, selected at random, is a prime number. To calculate this, we need to identify all prime numbers less than 50 and then divide that count by the total number of positive integers less than 50, which is 49 (since we only consider positive integers greater than 0).
The prime numbers less than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. This gives us a total of 15 prime numbers.
Therefore, the probability that the integer is prime is 15/49. To express this as a decimal accurate to three decimal places, we perform the division: 15/49 ≈ 0.306, hence the probability is approximately 0.306.