Video: CBSE Class X • Pack 5 • 2014 • Question 6

CBSE Class X • Pack 5 • 2014 • Question 6

01:46

Video Transcript

If a number is selected at random from one to 30, what is the probability of selecting a prime number?

Let’s begin by recalling what we mean by a prime number. A prime number is an integer which has exactly two factors, one and itself. For this reason, one is not actually a prime number since it only has one factor. Let’s list out the rest of the numbers between one and 30 and find the ones that are prime.

Two is the only even prime number since its factors are one and two. The next three prime numbers are three, five, and seven. Nine is not a prime since it has factors of one and nine, but also three. 11, 13, 17, and 19 are the next four. A common mistake is to think that 21 is a prime number. However, the factors of 21 are one and 21, but also three and seven. In fact, the only prime numbers between 20 and 30 are 23 and 29. There’s a total of 10 prime numbers in that list.

Now remember, the probability of an event occurring is found by calculating the number of ways for the event to occur and dividing it by the total number of outcomes. For this question, we’re dividing the total number of prime numbers by the total amount of numbers all together. That’s 10 divided by 30. We can simplify this fraction by dividing both the numerator and the denominator by 10. And we get that the probability of selecting a prime number is one-third.

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