Probability Of Drawing A Heart

Rocky D.

asked • 10/31/20

What is the probability of drawing a heart from a deck of cards on the first draw and not drawing a heart on the second draw without replacement?

1 Expert Answer

First, we have to find the probability of drawing a heart. So we know that in a 52 card deck, there are 13 hearts, so our probability of drawing a heart on the first try is 13/52. So now, we are left with 51 cards after drawing a heart, so we would have 12/51 cards be hearts, while the rest (39/51) are non-hearts. So P(H N Non-H)= P(H)*P(Non-H|H)= 13/52*39/51= 507/2652 = 13/68. I hope this helped.

Rocky D.

I'm confused Because the likelihood of getting a card not a heart is greater than a heart. Initially the heart probability was 0.25 and this equations gives the probability of 0.191 which is less. But just 39/51= 0.76 chance which seems more likely? In your calculation We multiply the two together because it's an and correct? So it would NOT just be 39 (cards that are not hearts) / 51 (cards left on deck) 39/52

Deontae H.

tutor

Yes because you are picking the cards in sequential order. It's very similar to the permutation concept. So the rest of the cards that are not hearts is 39 and you're picking from 51 cards, because the rest of the cards plus the 12 remaining hearts gets you 51. So 39/51 would be the probability that you pick a card that is not a heart given your first selection was a heart.

Rocky D.

Deontae H.

tutor

Yes, because you're multiplying the probabilities out, since you want the chance of both events happening.

Rocky D.

Thank you very much!!

Deontae H.

tutor

No problem man. I hope you understand the concept!

Rocky D.

Yes I do now. Thank you. I was coming up with both as I stated and wasn't sure which was the correct process. Your clarification was great! Thank you soo much!

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