playing card probability...please help?

We pick 5 cards one after the other. We look at the card and put it back and shuffle. What are the chances that the 5 cards are hearts? are aces? are faces? that there will be 2 hearts, a spade, a club and a diamond? that there are two hearts?

Now do the same but without putting back the card after looking at it.

Any help would be apprecitated. thanks so much!

1 Answer

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  • 1 decade ago
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    P(all hearts)

    =(1/4)^5

    P(all aces)

    =(1/13)^5

    P(all faces)

    =(3/13)^5

    P(2h,1s,1c,1d)

    =(1/4)^5

    P(2h)

    =(1/4)^2 * (3/4)^3

    no replacement

    P(all hearts)

    =13*12*11*10*9 / 52*51*50*49*48

    =13!47! / 52!8!

    =33/49*17*80

    =33/66640

    P(all aces)

    =4*3*2*1*0 / 52*51*50*49*48

    =0

    since there's not enough aces to start with (only have 4 when you want 5)

    P(all faces)

    =12*11*10*9*8 / 52*51*50*49*48

    =12!47! / 52!7!

    =3*11 / 13*17*49*10

    =33/108290

    P(2h,1s,1c,1d)

    =13^4 *12 / 52*51*50*49*48

    =13^3/16*51*50*49

    P(2h)

    =13*12*39*38*37 / 52*51*50*49*48

    =13*19*37 / 8*17*50*49

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