How to Find The Probability of Drawing 2 cards Without Replacement

Learn how to find the probability of drawing 2 cards without replacement. I show you 3 examples of how to easily find the probability of drawing 2 face cards, drawing 2 hearts, and drawing 3 aces.

Time Stamps
0:00 Probability of drawing 2 face cards without replacement
2:45 Probability of drawing 2 hearts without replacement
4:27 Probability of drawing 3 aces without replacement

[danielmitchem]

What's the probability that the first one you draw is incorrect but the second one is correct? In other words, I want to draw an ace but the first time I draw, I get a heart. The second time I draw, I get the ace. What is that probability? Thanks so much for the video!

[sukainahrawashdeh]

Two cards are drawn successively and without
replacement from an ordinary deck of playing cards.
Compute the probability of drawing :A heart on the first draw and an ace on the second draw.

[nicholasrobinson]

cant beleve the advice i needed was " just pretend the one you took WAS a face card " I was overthinking it

[STEMproof]

Since this is WITHOUT REPLACEMENT, this implies that F, F are DEPENDENT events.
QUESTION: Why are you using the Multiplication Rule for INDEPENDENT events?
"P(Heart and Heart) = P(Heart)P(Heart) = (13/52)(12/51)

If you are using the DEPENDENT form of the Mult. Rule:
P(Heart and Heart) = P(Heart)P( Heart | Heart), could you please explain how you got:
P( Heart | Heart ) = 12/51 ?

I'm confused on this since P( Heart | Heart ) = P( Heart AND Heart) / P(Heart), how did you get
P( Heart AND Heart) / P(Heart) = 12/51? I do not understand how to get 12/51 from this.

I understand the reasoning clear enough (13 - 1) = 12 and 52 - 1 = 51. but how do you get 12/51 out of the intersection divided by P(Heart)?

Thank you.

[BillFeinberg]

Probability of drawing a face card, no replacement, and then drawing a heart. Trying to figure out what to do with the overlap of a face that is a heart

[-Bloomingtales]

I really hate statistics and hate that we’re forced to take this ridiculous class …

[myjourneythroughbreastcanc]

What is the probability that the first is a Club and the second is a Heart, without replacement?