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 king.

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 a red card when a card is drawn from a standard card deck. So in order to solve this problem, let's think about what a standard 52 card deck looks like. So standard 52 card deck has four suites. It has clubs, spades, diamonds and hearts. And in this case the diamonds and the hearts are red. And within each of those suites there's an ace Cards two through 10 and a jack, a queen and a king. This means that each of the suites have 13 cards. So because there's two red suites in a standard 52 card deck, there's two times 13 amount of red cards in a standard 52 card deck or red cards. So now that we've determined the total number of red cards, we can think about the probability of not obtaining a red card. So the total number of outcomes is 52 because there's 52 cards total. So 52 is the total amount of outcomes or total number of outcomes. And in this case because we're looking for the probability of not obtaining a red card, we can solve this two ways. We can either say that 26 is equal to the number of favorable outcomes. Because if we take away the 26 red cards from 52, we get that there's still 26 block cards in the deck. So 26 is still the number of favorable outcomes. So you can say the probability of not obtaining a red card is the number of favorable outcomes 26 divided by the number of total outcomes 52. And if we simplify that, that simplifies to one half, we can also solve this by saying that The probability of pulling any card is one But we want to subtract the probability of pulling a red card, which is again the number of red cards, 26 divided by the number of total cards, which is 52. And once again 26 divided by 52 simplifies to one half. So I can rewrite this as 1 -1 half, which again leaves one half. So these are two methods of getting the same answer the same probability and They both say that one half is the probability of not obtaining a red card when we pull from a standard 52 card deck and you can see that that aligns with answer choice B. So hopefully this video helped and see you next time