A deck of cards is shuffled and a card is drawn

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21. A deck of cards is shuffled and a card is drawn. Determine each of the following probabilities. a) The probability that a face card is selected. b) The probability that the card is not a 7. c) The probability that the card is a Club. d) The probability that a Red face is selected. e) The probability that the card is Red or a King. f) The card is red or a Club. 22. Two dice (one red and one green) are to be rolled. The sample space consists of the 36 outcomes listed below. The first number is what is rolled on the Red die and the second number is what is rolled on the Green. Determine: a) P(At least one of the dice is a 5) b) P(Sum of the dice is equal to 7) c) P(Sum of the dice is 11 or more) d) P(Both are less than 3) e) P(Red is larger than Green) f) P(Sum is greater than 9) g) P(Red = 6) h) P(Largest number is a 5) i) P(Smallest number is a 5) 1,1 1,2 1,3 1,4 1,5 1,6 2,1 2,2 2,3 2,4 2,5 2,6 3,1 3,2 3,3, 3,4 3,5 3,6 4,1 4,2 4,3 4,4 4,5 4,6 5,1 5,2 5,3 5,4 5,5 5,6 6,1 6,2 6,3 6,4 6,5 6,6 S
Section 2.6 Counting Techniques 23. Five coins are to be tossed. Determine the cardinality of the sample space. 24. A coin is to be tossed followed by rolling two dice. Determine the cardinality of the sample space. 25. Two dice are to be rolled and the total number of spots viewed are our outcomes. Determine the cardinality of the sample space. Are these outcomes equally likely? 26. Three dice are to be rolled. Determine the cardinality of the sample space. 27. How many ways can we arrange 7 red chips and 4 blue chips in 11 slots? 28. How many ways can we arrange 5 white chips, 4 blue chips and 3 red chips in 12 slots?
30. Suppose that we have 9 distinct objects to put in 9 slots and that the 9 slots are partitioned into 3 groups. The first group has 3 slots, the second has 2 slots and the third has 4 slots. How many ways can we put the objects in the slots if we do not care about the order in which they got into the groups? ___ ___ ___|___ ___|___ ___ ___ ___ 31. Three cards are selected from a deck of 52 cards. Determine the probability that they are all face cards. 32. A bin contains 10 red chips, 8 white chips and 2 blue chips. Three chips are selected without replacement. Determine: a) The probability that all three chips are white. b) The probability that all three chips are red. c) The probability that all three chips are blue. 33. Four cards are selected from a deck of cards. Determine the probability that all four of them are hearts. 34. Four cards are selected from a deck of cards. Determine the probability that all four of them are red. 35. Four cards are selected from a deck of cards. Determine the probability that all four of them are Jacks. Section 2.7 Conditional Probability
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