1. Consider a standard deck of playing cards from which you draw five cards with
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Question
1. Consider a standard deck of playing cards from which you draw five cards without replacement a. Find the probability of drawing all numbered cards (2,34,5,6,7,8,9 and 10). b. Find the probability of drawing exactly two Jacks, two Kings, and a number between 4 and 8 (inclusive) c. Find the probability of drawing at least one card of each suit 2. Suppose in a bag there are 8 black, 5 gold, and 7 white chips from which you draw three with replacement. Find the probability you draw one chip of each color. Find the probability you draw exactly 2 black chips, knowing the first chip was black Find the probability you draw at least one gold chip. a. b. c. Consider a fair four-sided die with possible values x e (1,2,3,4). You are interested in X, the sum of two independent rolls of this die. 3. a. Define the PMF of X b. Find P(X = 5 1 XExplanation / Answer
1. a) The exhaustative cases 52C5 = 2598960
The favourable cases 4*9 = 36C5 = 376992
Required Probability = 379992 / 2598960 = 0.14505
b) P(2 jacks, 2 kings, number between 4 and 8) = (4C2 * 4C2 * 4*5C1) / 52C5 = 6*6*20 / 2598960 = 0.000277
c) P(at least one card of each suit) = (13C1 * 13C1 * 13C1 * 13C1 * 52C1) / 52C5 = 0.571448
2.
2.
a) The probability that one chip from each color = 8/20 * 5/20 * 7/20 = 0.035
b) P(exactly 2 black chips/first chip was black) = 8/20 * 8/20 = 0.16
c) The probability that at least one gold chip is = 1 - (15/20)*(15/20)*15/20) = 0.578125
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