1. Consider a standard deck of playing cards. There are 52 cards in the deck wit

Question

1. Consider a standard deck of playing cards. There are 52 cards in the deck with 13 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 (king), and A (ace). Suppose three cards are drawn at random from the deck without replacement. a) What is the probability of event A that all cards are of the same rank? (6 pts.) b) What is the probability of event B that none of the three cards is a spade? (6 pts.) c) Are events A and B independent or dependent? Justify your answer with ), Q (queen), K

Explanation / Answer

We know that, about information of deck of playing cards.

Total 52 cards,

a) A event all cards same rank, P(A)=13/52

P(A)=1/4.

b) B event none of three cards is spade.

P(B)=10/52

P(B)=0.19.

C) events A and B are dependent. Because common element 3 spade , P(A intersection B)=3/13. So that events A and B are dependent.

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