A teacher wrote the numbers from 10 to 20 on number cards and asked a Grade 9 learner to select a card at random. Determine the probability that the number of the card picked is:

(a) a prime number;

(b) an even number.

The probability of picking a prime number from the cards numbered 10 to 20 is 11 4 ​ , and the probability of picking an even number is 11 6 ​ .
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Answered by Anonymous | 2025-07-14

Let's start by finding the probability of selecting a prime number from the numbers 10 to 20.
(a) Probability of selecting a prime number:
The numbers from 10 to 20 are: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.
A prime number is a number greater than 1 that has no divisors other than 1 and itself.
Within this range, the prime numbers are:

11

13

17

19


So, there are 4 prime numbers.
To find the probability, divide the number of favorable outcomes (prime numbers) by the total number of possible outcomes (all numbers from 10 to 20).
Total numbers from 10 to 20: 11
So, the probability is: P ( prime ) = 11 4 ​
(b) Probability of selecting an even number:
Even numbers are those which can be divided by 2 without leaving a remainder.
The even numbers from 10 to 20 are:

10

12

14

16

18

20


So, there are 6 even numbers.
To find the probability, divide the number of favorable outcomes (even numbers) by the total number of possible outcomes (all numbers from 10 to 20).
So, the probability is: P ( even ) = 11 6 ​
In conclusion, the probability of picking a prime number is 11 4 ​ and the probability of picking an even number is 11 6 ​ . These probabilities are calculated by counting the outcomes that match the criteria (either being a prime or an even number) and then dividing by the total number of possible choices (11 cards in total).

Answered by OliviaLunaGracy | 2025-07-21