A standard deck of playing cards is well shuffled, and three cards are selected at random without replacement.?

Question

Find the probabilities of the following events:
a. A=Three hearts are chosen
b. B=Exactly two red cards are chosen
c. C=At least one 10 is chosen (Hint: Consider C'.)
d. D=Three face cards are chosen
e. A intersection D
f. E=Three aces or three kings are chosen

C · Accepted Answer

a.  P(H and H and H) = (13/52)(12/51)(11/50)

b. P(R and R) = (26/52)(25/51)

c.  P(one or more 10's) = 1 - P( no 10's) = 1 - 48/52

d.  P(F and F and F) = (12/52)(11/51)(10/50)  where F = King, Queen, Jack

e. P(H and H and H) AND P(F and F and F) = P( K of H and Q of H and J of H )  Now this one gets complicated because there are many ways to draw a heart that is also a face card...KQJ or QKJ or QJK or KJQ or JKQ or JQK.  So do the 1st one and then multiply by 6 since there are six ways to draw these cards:  6(1/52)(1/51)(1/50)

f.  P(AAA or KKK) = P(AAA) + P(KKK) = 2 times (4/52)(3/51)(1/50

I'll leave it to you to do the multiplication.

Polygon · Answer

a. A=Three hearts are chosen
(13/52)*(12/51)*(11/50)

b. B=Exactly two red cards are chosen
(26/52)*(25/52)

c. C=At least one 10 is chosen (Hint: Consider C'.)
(4/52)
d. D=Three face cards are chosen
At least K,Q or J
(12/52)*(11/51)*(10/50)

e. A intersection D
f. E=Three aces or three kings are chosen
(8/52)*(7/51)*(6/5)

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A standard deck of playing cards is well shuffled, and three cards are selected at random without replacement.?

2 Answers