Card games

Question

draw five cards from a standard deck and get

a) four aces

b) three aces and two jacks

c) three aces and a pair

Update:

why multiplying 10?

Answer 1

Favorite Answer

Say the probability for incedent E to occur as P(E).

P(4 Aces)=4/52*3/51*2/50*1/49*5=1/54145=0.001847%(4 sig. fig.)

P(3 Aces + 2 Jacks)=4/52*3/51*2/50*4/49*3/48*10=1/108290=0.0009234%(4 sig. fig.)

P(3 Aces + Pair)=4/52*3/51*2/50*48/49*3/48*10=6/54145=0.01108%(4 sig. fig.)

Answer 2

why multiplying 10?

Think about when two jacks and three aces are filled into 5 boxes, how many arrangements can there be.

J J A A A

J A J A A

J A A J A

J A A A J

A J J A A

A J A J A

A J A A J

A A J J A

A A J A J

A A A J J

or by binomial distribution,

5C2 = 10