Question

An integer is chosen at random from 1 to 20. What is the probability that it is a prime number?

• A. 0.4
• B. 0.5
• C. 0.2
• D. 0.3

Hint:

Remember: 1 is not a prime number.

Answer 1

The Correct Option is A

To find the probability that a randomly chosen integer from 1 to 20 is a prime number, we first need to identify all the prime numbers within this range.

A prime number is defined as a number greater than 1 with no positive divisors other than 1 and itself.

Let's list the integers from 1 to 20 and identify the prime numbers:

1. The integers from 1 to 20 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
2. Prime numbers from this list are: 2, 3, 5, 7, 11, 13, 17, 19.

There are 8 prime numbers between 1 and 20.

The total number of integers in the range is 20.

Probability is calculated by the formula: \(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\)

Substitute the values:

\(\text{Probability} = \frac{8}{20}\)

Simplify the fraction:

\(\frac{8}{20} = \frac{2}{5}\)

Converting to decimal form:

\(\frac{2}{5} = 0.4\)

Therefore, the probability that a randomly chosen integer from 1 to 20 is a prime number is 0.4.

Hence, the correct answer is 0.4.