In Exercises 39–44, you are dealt one card from a 52-card deck. F...

Question

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.

Accepted Answer

Hello, everyone in this video, we're going to be looking at this practice problem where we want to find the probability of not obtaining an ace when a card is drawn from a standard 52 card deck. So not to get started. Let's think about what a standard 52 card deck looks like. So a standard 52 card deck has four suites, it has clubs, diamonds, hearts and speeds. And within each of those suites there's an ace And the cards two through and after 10 there's a jack, a queen and a king. So because each of the suites has one ace, that means that there's four ace total in a 52 card deck. So that means that the probability of pulling an ace is the amount of ace present, which is four divided by the total amount of cards, which is 52. But if we go back to the question, we don't want the probability of pulling an ace, we want the probability of not pulling an ace. So in order to find the probability of not playing nice, we can subtract the probability of pulling an ace from the probability of pulling any card. So the probability of pulling any card is simply 52/ because we don't care about what card we're going to pull. We're just know that it's going to happen. So notice how 52 divided by 52 is the same thing as one. So I can write this as one -4 divided by 52. So now this is telling me the probability of not pulling an ace. And from here we can actually actually simplify four divided by 52 as one divided by 13. So this becomes 1 -1, divided by 13 or 12 divided by 13. So 12 divided by 13 becomes the probability of pulling a card that is not an ace, and you can see that that aligns with answer choice D. So hopefully this video helped and see you next time.

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.

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