You are dealt one card from a 52-card deck. Find the probability ...

Question

You are dealt one card from a 52-card deck. Find the probability of getting an ace or a king.

Accepted Answer

Welcome back. I'm so glad you're here. We've got this odd game of two sets of a 54 card deck. So not a 52 card deck that we normally talk about this one is a 54 card deck that includes two jokers. Okay, two sets of 54 card decks real quick. We'll just note that we're talking about 108 cards here. You win this game if you get either a joker or a jack. So what's the probability of winning? Okay first let's think about this for a moment. And are these mutually exclusive events? If you draw a joker, can you be drawing a jack at the same time? These are mutually exclusive, You cannot draw a joker and simultaneously be drawing a jack or draw jack and simultaneously be drawing a joker. One card has to be one or the other. So we recall from previous lessons that when we've got mutually exclusive events, that's the probability of a event or excuse me or event B occurring. Then we take the probability of event A and add it to the probability of event B. And that will give us the probability that you win in this case. So let's think about this probability of getting a joker. Okay, what do we know about Joker's? Well, 54 card deck includes two jokers. So that means this 108 Card deck would have twice that there will be four jokers. Alright and now how about the probability of getting a jack. Well a 52 card deck has four jacks. So in two sets we'd be talking about eight out of these 108 cards, add those together, we can go straight across because they have a common denominator. We've got 12 out of 108 or we can reduce that, they're both divisible by 12 and that gives us 1/9. We look at our answer choices and that matches with answer choice. C. Well done, we'll catch you on the next one.