Probability of playing cards?

Three cards are drawn succession with replacement from a deck of 52 cards what is the probability that the third card is a spade, given that the first two cards drawn were not spades?

Probability of playing cards?
Probability that a card drawn is a spade:


4/52 or 1/13


Probability that a card drawn is not a spade:


(52-4)/52 or 12/13





1st draw not spade * 2nd draw not spade * 3rd draw spade


=(12/13) * (12/13) * (1/13)


you can solve the rest ;)





Hope this helps
Reply:25% is the probability that the third card is a spade.


Due to replacement, you will have the same probability on


the 2nd %26amp; 3rd draws as you did on the first draw.Beginning probability was 13/52 = 25%





By using replacement %26amp; I presume re-shuffling, you have


created conditions similar to rolling dice. All probabilities


would remain constant.





Asking the probability of a specific draw, with replacement,


makes that draw a single event. Would be quite different if


question were: Probability of a spade not being drawn in


three CONSECUTIVE draws? The event would then be


comprised of three actions.( 3/4*3/4*3/4) = 27/64 or


42.1875%
Reply:not a spade(3/4) not a spade(3/4) and spade(1/4)





=.1406 so a 14.1% chance of that occuring

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