+0  
 
0
524
3
avatar+82 

What is the probability that a hand of five cards will contain at least one king?

yuhki  Nov 21, 2014

Best Answer 

 #3
avatar+17744 
+5

Another way to get CPhill's answer:

Still using his idea of subtracting the probability of getting no kings from 1, the total possible probability.

The only way that you can get no kings is:

to get no king for the first card:  probability = 48/52    

to get no king for the second card:  probability = 47/51

to get no king for the third card:  probability = 46/50

to get no king for the fourth card:  probability = 45/49

and, finally:

to get no king for the fifth, and last, card:  probability = 44/48

Multiplying all these probabilities together:  48/52 x 47/51 x 46/50 x 45/49 x 44/ 48  =  0.6588

Subtracting this from 1.000:  1.000 - 0.6588  =  0.341

geno3141  Nov 22, 2014
 #1
avatar+7188 
0

2 jokers,  4 aces, 4 2's, 4 3's, 4 4's, 4 5's, 4 6's, 4 7's, 4 8's, 4 9's, 4 10's, 4 jacks, 4 queens, and 4 kings

 

I'm not good with probabiltiy...but in 54 cards....there are 4 kings,  so maybe 4/25 because their are 5 cards in the hand....like I said,  not good, giving my best try

 

What's up with all these probability problems?

 

happy7  Nov 21, 2014
 #2
avatar+87333 
+5

This equals..... [1 - probability of no kings ]

So, the ways to choose no kings is to just select 5 cards from the remaining 48

This is ginen by  C(48,5) = 1712304

And the total way of selecting 5 cards from 52 is C(52,5) = 2598960

So....the probability of at least one king is

1 - 1712304/2598960 = about 34.1%

 

CPhill  Nov 21, 2014
 #3
avatar+17744 
+5
Best Answer

Another way to get CPhill's answer:

Still using his idea of subtracting the probability of getting no kings from 1, the total possible probability.

The only way that you can get no kings is:

to get no king for the first card:  probability = 48/52    

to get no king for the second card:  probability = 47/51

to get no king for the third card:  probability = 46/50

to get no king for the fourth card:  probability = 45/49

and, finally:

to get no king for the fifth, and last, card:  probability = 44/48

Multiplying all these probabilities together:  48/52 x 47/51 x 46/50 x 45/49 x 44/ 48  =  0.6588

Subtracting this from 1.000:  1.000 - 0.6588  =  0.341

geno3141  Nov 22, 2014

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.