Math Games

Question: This is a hard math question?

"Euchre is a popular card game played with a partial deck of ordinary cards. Only 24 cards are used: the 9, 10, Jack, Queen, King, and Ace of each suit (hearts, spades, diamonds, and clubs). Consider the experiment of drawing cards from a Euchre deck until a club is drawn. After each draw the card is replaced and the deck is shuffled." Then it asks "complete the table below for a theoretical probability distribution for the number of draws to get a club. The first column in the table reads "number of draws to get first club" and the values are 1, 2, 3, 4, 5, 6 or more i'm supposed to find the probability for each value.

Answer: For every draw, there are 6 clubs out of 24 so the prob of drawing a club is 1/4.
And since you put back the card you drew, it remains 1/4.

P(first draw) = 1/4
P(second draw) = (3/4)*(1/4) (it's a 3/4 prob you didn't draw a club the first time)
P(third draw) = (3/4)^2*(1/4) (it's a (3/4)^2 prob you didn't draw a club the first and 2nd times)

In general, P(on draw n) = (3/4)^(n-1)*(1/4)

Math Fluency pt.2: Math Games

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