Combinatorics select 3 cards out of 52, probability all 3 spades and not. You get 3 cards out of 52

cooloicons62 2022-07-13 Answered
Combinatorics select 3 cards out of 52, probability all 3 spades and not.
You get 3 cards out of 52, the order doesn't matter.
a) What is the probability all 3 cards are spades?
b) What is the probability none of the 3 cards are spades?
a) I think it is
( 13 3 ) ( 52 3 ) 0.012941
b) I know it is
= ( 39 3 ) ( 52 3 ) 0.41353
I know P ( A c ) = 1 P ( A )
And if a is A and b is A c the equation above is not correct..
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Answers (2)

Karla Hull
Answered 2022-07-14 Author has 20 answers
Let P(n) be the probability that n cards are drawn. P(3) is the answer for a), and you got that right. The answer for b) is P(0).
P ( 0 ) + P ( 1 ) + P ( 2 ) + P ( 3 ) = 1, so P ( 0 ) + P ( 3 ) < 1
P ( n ) = ( 13 n ) ( 39 3 n ) ( 52 3 )
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Ximena Skinner
Answered 2022-07-15 Author has 7 answers
The issue here is that the complement of the event "all of the 3 cards are spades" is "at least one of the 3 cards is not a spade" not "none of the 3 cards are spades".
So, P ( all of the 3 cards are spades " ) + P ( none of the 3 cards are spades " ) < 1
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