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#1
01-28-2018, 05:24 PM
 ubhutto SOA Join Date: Oct 2013 College: St. John's university Posts: 11
Simple Probability Problem

Hi Everyone

I had a relatively simple problem that for some reason i can't get my head around.

The problem states:

If two cards are drawn from a deck then what is the chances that the sum of the two is 21?

face card = 10
ace = 11

I got the solution but i just don't understand how they did it. can someone explain it to me.

Thank you in advance for your help.
#2
01-28-2018, 06:55 PM
 Marcie Member CAS Join Date: Feb 2015 Posts: 8,853

Quote:
 Originally Posted by ubhutto Hi Everyone I had a relatively simple problem that for some reason i can't get my head around. The problem states: If two cards are drawn from a deck then what is the chances that the sum of the two is 21? face card = 10 ace = 11 I got the solution but i just don't understand how they did it. can someone explain it to me. Thank you in advance for your help.
How did you get the solution?

They probably did something similar.
#3
01-28-2018, 07:06 PM
 ubhutto SOA Join Date: Oct 2013 College: St. John's university Posts: 11

Quote:
 Originally Posted by Marcie How did you get the solution? They probably did something similar.
They just gave a number but not how to get to it, any idea how to work it out?
#4
01-28-2018, 08:15 PM
 Marcie Member CAS Join Date: Feb 2015 Posts: 8,853

Quote:
 Originally Posted by ubhutto They just gave a number but not how to get to it, any idea how to work it out?
Very carefully?
#5
01-28-2018, 08:26 PM
 Marcie Member CAS Join Date: Feb 2015 Posts: 8,853

Quote:
 Originally Posted by ubhutto They just gave a number but not how to get to it, any idea how to work it out?
Is the answer about 4.83%? (i.e 32/663)

If so, then yes. If not, I need to review my probability.
#6
01-28-2018, 08:45 PM
 royevans Member SOA Join Date: Jul 2017 Posts: 465

There are 12 face cards (4 jacks, 4 kings, 4 queens) and 4 aces and 4 10's.

Number of pairs involving those above combinations is (16*4) * 2 = 128.
Number of total two card combinations = 52 * 51 = 2652

Pr(sum = 21) = 128/2652= 0.04827?

Oh boy...
#7
01-28-2018, 10:20 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,226

Alternatively there are two sequences (10,11) and (11,10). Sum the two probabilities.

 Tags probability

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