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# Probability with Venn diagrams

Want to learn some probability? This video explains the probability of drawing a Jack or a Heart from a deck of 52 cards. It uses a Venn diagram to illustrate the concept of overlapping events and how to calculate the combined probability. Key definitions include "equally likely events" and "overlapping events". Created by Sal Khan.

## Want to join the conversation?

• Maybe this is explored later in the play list but is it just coincidence that P(J and H) = P(J)*P(H) or can we always use this? I know he goes on to show the formula for P(A or B) but was wondering about the formula for P(A and B).
• It is not a coincidence. It is the same thing.

For P(J and H) you can simply count within the deck the number of Jacks that are also Hearts, like in the video, and you'll get 1/52. Or you can look at the chances of picking a Jacks, and out of those jacks, what are the chances of choosing one that is a Hearts.

If I look at the chances of grabbing a Jacks, P(J), we get that there are 4 Jacks in the deck, so 4/52 = 1/13. And now, out of those four Jacks, how many are Hearts? Only one, so we get a probability P(H) of 1/4 to pick one card that is Hearts. This means that there is a 1/4 chance within the 1/13 chance to get a Hearts that is also a Jacks. This is represented by multiplying both probabilities (1/13)*(1/4) or P(J)*P(H) like you stated. You're essentially applying a probability to another probability. :)
• In the first example the answer is 1/13. Isn't that means that if you randomly draw 13 cards from the deck then at least 1 card is a Jack?
• No, This is not necessary. Probability of 1/13 means that if we keep drawing out 13 cards at random, then on an average we should have one jack per lot of 13 drawn out. The whole point of Probability is that there is one chance out of every 13 chances that the card drawn out is a jack. In fact, in the worst case scenario, its very much possible that out of 52 cards, we draw out 48 cards one by one, and not one of them is a jack!
But then we'll compulsorily have to draw jacks on the next 4 turns, so finally the probability turns out to be 1/13 only.
• A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart ?
• there 1 "queen of club" and 1 "king of heart" so
the probability a queen of club is 1/52 because there is only one in the neck.
and the probability a king of heart is 1/52 because there is only one in the neck.
1/52 + 1/52 = 2/52 = 1/26
there for you have a probability of 1/26 to get a queen of club or a king of heart.
• 1. In a standard deck of cards, find the probability of selecting a club or an ace on a single draw.
• In a 52 card deck there 13 cards of clubs and 4 aces. So, on a single draw the probability of selecting a club is 13/52 and the probability of selecting an ace is 4/52.
If you want the probability of selecting a club or an ace you should be carefull not count the ace of clubs twice. The probability is then 16/52 (13 clubs + 4 aces - ace of clubs)
Sometimes 40 card decks are used instead (10 cards of clubs and 4 aces). In that case the probability of selecting a club is 10/40 and the probability of selecting an ace is 4/40. The probability of selecting a club or an ace is then 13/40 (10 clubs + 4 aces - ace of clubs)
• HI, I thought P(J or H) would be = P(J) + P(H). In this case, 1/4 + 1/13. Why not?
• P[J or H]=P[J]+P[H]-P[J and H],because P[J and H] repeat.
• what does mutually exclusive mean ??
• Two events are mutually exclusive if they cannot occur together.
• Around ish where we add the two sets {4/52}A{13/52} ie; (4+13)/(52) and then proceed to subtract the shared set, I believe we should be subtracting the fractional {1/52} instead of 1 - this would fit our answer more appropriate to convention. Mathematically speaking, subtracting a unit of one from a fraction is the same as negating the fraction by a unit whole based on its denominator.

So in this case, our equation would be :
=>P(j) + P(h) - P(j + h) = P(j or h)
=>4/52 + 13/52 - 1 ~ 4/52 + 13/52 - 52/52
=>17/52 - 52/52 => -(35/52)
.:.P(j or h) = -35/52

which doesn't make sense. So in order for this to be accurate, we need to be subtracting 1/52, which would give us (17/52) - (1/52) = 16/52 = 4/13
• Yes, the answer is 16/52, Sal says and writes out this fact. The "-1" is in the numerator, he just didn't extend the fraction bar all the way.
• why isn't the joker card being used ?
• Just so it's consistent no matter the deck. A deck may have more than 1 joker card, or none at all. All decks have the base 52 though.