SOLUTION: From a shuffled standard deck of cards, 8 cards are dealt to a player. Let A= event that exactly 3 cards are red B= event that exactly 3 cards are face cards (K, Q, J) C= event

Algebra ->  Probability-and-statistics -> SOLUTION: From a shuffled standard deck of cards, 8 cards are dealt to a player. Let A= event that exactly 3 cards are red B= event that exactly 3 cards are face cards (K, Q, J) C= event       Log On


   



Question 1159829: From a shuffled standard deck of cards, 8 cards are dealt to a player. Let
A= event that exactly 3 cards are red
B= event that exactly 3 cards are face cards (K, Q, J)
C= event that exactly 5 cards are spades
Determine the following probabilities:
a. P(A)
b. P(B)
c. P(C)
d. P(AB) (Hint: Express the events as a union of mutually exclusive events, each event
describing how many red face cards, black face cards, red non-face cards, black nonface cards)
e. P(AC)
f. P(BC)
g. P(ABC)
h. P(A∪B∪C)

Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
a. P(A)
%2826C3+%2A+26C5%29%2F%2852C8%29 = = 11440%2F50337 = 0.2273

b. P(B)
%2812C3+%2A+40C5%29%2F%2852C8%29 = = 123728%2F643195 = 0.1924

c. P(C)
%2813C5+%2A+39C3%29%2F%2852C8%29 = = 100529%2F6431950 = 0.0156

d. P(AB)



=

= %28310080+%2B+8721000+%2B+19494000+%2B+4332000%29%2F752538150

= 32857080%2F752538150

= 1095236%2F25084605

= 0.0437

e. P(AC)
%2826C3+%2A+13C5%29%2F%2852C8%29 = = 572%2F128639 = 0.0044

f. P(BC)



=

= %28182700+%2B+1409400+%2B+680400+%2B+21168%29%2F752538150

= 2293668%2F752538150

= 9802%2F3215975

= 0.0030