A standard card deck consists of 52 cards each card has a...

Name: a standard card deck consists of 52 cards each card has a rank 2 3 4 5 6 7 8 9 10 j q k ace and a suit clubs diamonds hearts and spades 13 ranks 4 suits 52 cards suppose you are given 5 cards from the
Uploaded: 2023-02-07T05:09:16-08:00
Duration: 4 min 48 s
Channel: Audrey Fong
Description: a standard card deck consists of 52 cards each card has a rank 2 3 4 5 6 7 8 9 10 j q k ace and a suit clubs diamonds hearts and spades 13 ranks 4 suits 52 cards suppose you are given 5 cards from the

A standard card deck consists of 52 cards. Each card has a “rank”: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, Ace, and a “suit”: clubs, diamonds, hearts, and spades (13 ranks × 4 suits = 52 cards). Suppose you are given 5 cards from the deck. To calculate probabilities, you divide the number of ways in which something can happen by the total number of possible ways. (1) How many combinations are there where you get four aces? What is the probability that you get a poker hand with four aces? (2) How many combinations are there where you get four cards of the same rank (“four of a kind”)? What is the probability that you get a “four of a kind”?

Transcript

00:01 This question is given a standard that are 52 playing cards.

00:04 Part a, one to find probability the top card is a heart.

00:09 That would be 13 hearts out of 52 probability.

00:14 And that would be 0 .25.

00:17 B, probability the top card is an ace of king.

00:21 N is times or is plus.

00:24 So probability the top card is an ace is four aces out of 52.

00:29 Or, all is a plus.

00:31 It's a king.

00:32 Now, ace and king are two mutually exclusive events.

00:34 Can just add by this.

00:36 There are four kings out of 52 and so the answer is two out of 13.

00:52 See probability the top card is spade and the second card is clubs.

00:57 Now this is akin to without replacement kind of question choosing two cards without replacement.

01:03 Probability the first class is spade is 13 of 52 and is times.

01:10 Second card is clubs.

01:11 In the second round there are 13 clubs but out of 51 cards 13 out of 204.

01:31 D probability the top card is spayed second is an ace so first card is spade is 13 out of 52 and second is an ace there are four aces out of in the second round only 51 there'll be 1 out of 51 in part e probability the top three cards are all spayed so the first card probability is a spade is 13 out of 52 and second is a spade.

02:07 In the second round there's only 12 spades left out of 51 cards left.

02:11 And third card is spade.

02:13 In the third round only 11 spades out of total of 50 cards left.

02:20 There'll be 11 out 850.

02:29 The last one f is interesting...

Question

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