(3 points) A deck consists of cards with 5 suits labelled A to Eand numbered ran
ID: 3049609 • Letter: #
Question
(3 points) A deck consists of cards with 5 suits labelled A to Eand numbered ranks from 1 to 11. Each card is equally likely to be drawrn. Suits A to C are red. Suits D to E are blue. A card is drawn at random from this deck. What is the probability of it being suit A? 1/5 What is the probability of it being suit A given that it is red? 1/3 What is the probability of it being suit A given that it is blue? What is the probability of it being suit A given that it has rank 1? 1/5 What is the probability of it having a rank less than or equal to 2? 10/55 What is the probability of it having a rank less than or equal to 2 given it has a red suit? 6/33 What is the probability of it having a rank less than or equal to 2 given it has a rank less than or equal to 9? 2/9 What is the probability of it having a rank less than or equal to 9 given it has a rank less than or equal to 2? Two cards are drawn at random from this deck (making a list, not a subset, of 2 cards). What is the probability that the second card is blue? What is the probability that the second card is blue given that the first card is red?Explanation / Answer
Solution:
total number of cards = 11 * 5 = 55
number of red cards = 11 * 3 = 33
nuber of blue cards = 11 * 2 = 22
probability of drawing first red card and then blue card = (33/55)(22/54) = 0.2444
probability of drawing both blue cards = (22/55)(21/54) = 0.1555
( a )
probability that the second card is blue = 0.2444 + 0.1555 = 0.3999
( b )
probability that second card is blue given that first card is red = 0.1555 / 0.3999 = 0.3888
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