Stat210 WorkSheet#2 Chapter#2

Transcription

1 1. When rolling a die 5 times, the number of elements of the sample space equals.(ans.=7,776) 2. If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet, the possible number of elements in the sample space equals. (Ans.=156).. 3. A coin is tossed : if it falls heads up, it is tossed again. If it falls tails up, a die is rolled. Draw a tree diagram and determine the outcomes A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble. 5. Two dice are thrown. Let E be the event that the sum of the dice is odd, let F be the event that at least one of the dice lands on 1, and let G be the event that the sum is 5. Describe the events EF, FG, EF c, and EFG. 1 S.Alhidairah

2 6. A pair of fair dice is rolled. The event that{ getting a difference of the two dice at least 3} equals : 7. Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and P( = 0.5. What is the probability that (a) Either A or B occurs?(ans.=0.8) (b) A occurs but B does not? (Ans.=0.3). (c) Both A and B occur? (Ans.=0) 8. A retail establishment accepts either the American Express or the VISA credit card. A total of 24 percent of its customers carry an American Express card, 61 percent carry a VISA card, and 11 percent carry both cards. What percentage of its customers carry a credit card that the establishment will accept? (Ans.=74%) 9. Sixty percent of the students at a certain school wear neither a ring nor a necklace. Twenty percent wear a ring and 30 percent wear a necklace. If one of the students is chosen randomly, what is the probability that this student is wearing (a) a ring or a necklace? (Ans.=0.4) (b) a ring and a necklace? (Ans.=0.1) 2 S.Alhidairah

3 10. A total of 28 percent of American males smoke cigarettes, 7 percent smoke cigars, and 5 percent smoke both cigars and cigarettes. (a) What percentage of males smokes neither cigars nor cigarettes? (Ans.=70%) (b) What percentage smokes cigars but not cigarettes? (Ans.=2%) 11. An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students that are in both Spanish and French, 4 that are in both Spanish and German, and 6 that are in both French and German. In addition, there are 2 students taking all 3 classes. (a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes? (Ans.=0.5) (b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class? (Ans.=0.32) 3 S.Alhidairah

4 12. Suppose that A and B are mutually exclusive events for which P ( A) 0.5 and P( 0.25 The probability that A occurs, but B does not occur equals.. (Ans.=0.5) Suppose that A and B are mutually exclusive events for which P ( A) 0.5 and P( 0.25 The probability that neither A nor B occurs equals.. (Ans.=0.25) Let A and B events with P( A) 0.5, P( 0.35 and P( A Find P( A (Ans.=0.75) 15. Let A and B events with P( A) 0.5, P( 0.35 and P( A Find P( A (Ans.=0.28) 16. Let A and B events with P( A) 0.4, P( 0.25 and P( A Find P( A (Ans.=0.1) 17. Let A and B events with P( A) 0.4, P( 0.35 and P( A Find P( A (Ans.=0.47) A company contains 20 men and 10 women of which half men and half women have brown eyes. The probability that a person chosen at random is a woman or has a brown eyes equals.. (Ans.=0.67) 19. Interest centers around the life of an electronic component. Suppose it is known that the probability that the component survives for more than 6000 hours is Suppose also that the probability that the component survives less than or equal 4000 hours is a) The probability that the life of the component is greater than 4000 hours equals.. (Ans.=0.96) b) The probability that the life of the component is less than or equal 6000 hours equals.. 4 S.Alhidairah

5 (Ans.=0.58) 20. If the probabilities that an automobile mechanic will service 3, 4, 5, 6, 7, or 8 or more cars on any given workday are, respectively, 0.12, 0.19, 0.28, 0.24, 0.10, and 0.07, the probability that he will service at least 5 cars on his next day at work equals.. (Ans.=0.69) Let A and B be events with P(A), P(, and P(A. Find : P(A... 2.P(A c )... 3.P( A die is loaded in such way that each odd number is twice as likely to occur as each even number. If E is the event that a number greater than 3 occurs on a single toss of the die. Find P(E). (Ans.=0.44) 23. The successful completion of a construction project require that a piece of equipment works properly. Assume that either the project succeeds (A 1 ) or it fails because of one and only one of the following: mechanical failure (A 2 ) or electrical failure (A 3 ). Suppose that mechanical failure is three times as likely as electrical failure, and successful completion is twice as likely as electrical failure. Find probability A 1. (Ans.=0.333) 5 S.Alhidairah

6 24. A company produces 1000 light bulbs with three machines A, B, and C. Some of these light bulbs are defectives as shown in the table: Machine Defective Non-defective A B C A component is drawn at random. Find: a) The probability that the component is non- defective and from machine A. (Ans.=0.270) b) The probability that the component is defective or from machine C. (Ans.=0.5) 25. The distribution of ages of CEOs is as followings: Age Frequency up 11 If a CEO is selected at random, find the probability that his or her age is: a) Between 31 and 40 (Ans.=0.08) b) Under 31(Ans.=0.01) c) Over 30 and under 51(Ans.=0.35) d) Under 31 or over 60(Ans.=0.36) 6 S.Alhidairah

7 26. Of all the murder victims in 2010 whose relation to the offender was known, 24.8% were killed by a family member and 53% by an acquaintance. The rest were killed by a stranger. What is the probability that a randomly selected murder victim was killed by a stranger? (Ans.=0.222) 27. At a particular fitness center, 64.1% of the members take at least one class, 18.6% work with a personal trainer, and 9.2% do both. If a member of the center is selected at random, what is the probability that she does neither? (Ans.=0.265) 28. Cheap Rentals has nothing but budget cars for rental. The probability that a car has air conditioning is 0.5, and the probability that a car has a CD player is The probability that a car has both air conditioning and a CD player is What is the probability that a randomly selected car has neither air conditioning nor a CD player? (Ans.=0.19) 29. Two dice are thrown.let A denote the event that the sum of the faces is 7, and B denote the event that the exactly one of the faces is 2. Find P(A (Ans.=0.389) 30. In a certain college, 24% of the students failed Mathematics, 12% of the students failed Chemistry, and 10% of the students failed both Mathematics and Chemistry. A student is selected at random. a) The probability that he failed Chemistry or Mathematics equals.. (Ans.=0.26) b)the probability that he did not fail in at least one of the two subjects (Ans.=0.9) 7 S.Alhidairah