A card is selected from a pack of cards numbered one to 19. What is the probability that the card has an odd prime number?
So here are 19 cards labelled one to 19. So we wanna know the probability, out of all of these cards, that the card that we would choose would be odd and prime.
So first, let’s go through and pick all the cards that are odd. So here are the odd cards. Odd numbers begin with one. And then it’s every other number: one, three, five, seven, nine, 11, 13, 15, 17, 19, and so on. So here are all of our odd numbers.
Now we’re trying to find the probability that a card is odd and prime. So we have to pick prime cards from this stack, the pink one, because we already know that these ones are odd. And they’re from the original pack of cards.
So out of these ones, which ones are prime? So a prime number is a natural number, which are the counting numbers one, two, three, four, five, and so on. So it’s a natural number greater than one that is only divisible by itself and one. So since a prime number is greater than one, we can already eliminate one.
Now all the other numbers are greater than one. So we already know that. So let’s begin with three now. Is it prime? So is it only divisible by itself and one? Yes, there’s no other number less than three that goes into it other than one. So now for five, is there another number that can go into five other than itself and one? No, so five is odd and prime. Now what about seven? Seven is only divisible by itself and one.
Now when we get to nine, however, nine is divisible by three. So it is not prime. 11 is prime because it’s only divisible by itself and one, same thing for 13. But for 15, it is also divisible by five. So it’s not prime. But 17 and 19 are both prime as well.
So out of the 19 cards, how many of them were odd and prime? One, two, three, four, five, six, seven. So seven out of the 19 cards were odd prime numbers. So our probability that the card has an odd prime number is seven nineteenths.