1. Consider a standard deck of playing cards. There are 52 cards in the deck wit
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Question
1. Consider a standard deck of playing cards. There are 52 cards in the deck with 13 cards of each of the four suits, hearts, spades, clubs, and diamonds. The heart and diamond cards are red; while the spade and club cards are black. Each suit has cards labeled, from the lowest rank to the highest, as 2, 3, ..., 10, J (jack), Q (queen), K (king), and A (ace). Cards J, Q, K are called face cards. Suppose three cards are drawn at random from the deck without replacement. a) What is the probability that exactly two cards are face cards? (8 pts.) b) What is the probability that the three cards are of mixed suits (that is, not all cards are of the same suit; for example, the cases of 2 spades +1 heart and 1 spade + I heart + 1 club are both considered cards of mixed suits)? (8 pts.) c) Given that exactly two cards are face cards, what is the probability that the three cards have the same suit? What can you say about the independence of these two events (justify your answer by appropriate calculation)? (9 pts.)Explanation / Answer
a)
There are total 4 *3 = 12 face cards in a deck we have to choose 2 face cards from 12 cards in 12C2 ways.
Probability that exactly two cards are face cards = ( 12C2 ) / (52C2)
Probability that exactly two cards are face cards = 0.0498
b)
Probability that the three cards are are of mixed suit = 1 - Probability that the three cards are are of same suit
= 1 - ( 13C3) * (1 /4 ) / (52C3)
= 1 - 0.00324
Probability that the three cards are are of mixed suit = 0.99676
For solution of part -c please post same question again
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