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Stat 101 – Sheet 8 (Solutions) King Saud University Almajmaa’h Engineering College STAT 101 1430/2009 --------------------------------------------------------------------------------------------------------------------------------------- Solution of Sheet (8) Probability 1. Briefly explain the two properties of probability. Answer: See page 64 2. Briefly describe an impossible event and a sure event. What is the probability of the occurrence of each of these two events? Answer: An event that cannot occur has zero probability; such an event is called impossible event. An event that is certain to occur has a probability equal to 1 and is called a sure event. That is, For an impossible event M: For a sure event C: P(M) = 0 P(C) = 1 Example: suppose a box contains 5 red balls, the probability of selecting a red ball randomly from the box is 1 and the probability of selecting one green ball from the box is zero 3. Briefly explain the three approaches to probability. Give one example of each approach. Answer: the three approaches to probability are: 1) Classic probability 2) The relative frequency concept of probability, and 3) The subjective probability concept. Examples are given in pages 65-70. Dr. SaMeH Page 1 Stat 101 – Sheet 8 (Solutions) 4. Briefly explain for what kind of experiments we use the classical approach to calculate probabilities of events and for what kind of experiments we use the relative frequency approach. Answer: we use the classic approach to calculate probabilities of events when an experiment has the same probability of occurrence (equally likely outcomes). And we use relative frequency approach when outcomes for the corresponding experiments are not equally likely and we can either use past data or generate new data to calculate approximate relative probability. If an experiment is repeated n times and an event A is observed f times, then, according to the relative frequency concept of probability: P(A) = 𝑓 𝑛 5. Which of the following values cannot be probabilities of events and why? 1/5 .97 −.55 1.56 5/3 0.0 −2/7 1.0 Answer: -.55 , 5/3, -2/7 6. Which of the following values cannot be probabilities of events and why? .46 2/3 −.09 1.42 .96 9/4 −1/4 .02 Answer: -.9 , 1.42, 9/4, -1/4 7. Thirty-two persons have applied for a security guard position with a company. Of them, 7 have previous experience in this area and 25 do not. Suppose one applicant is selected at random. Consider the following two events: This applicant has previous experience, and this applicant does not have previous experience. If you are to find the probabilities of these Dr. SaMeH Page 2 Stat 101 – Sheet 8 (Solutions) two events, would you use the classical approach or the relative frequency approach? Explain why. P( the applicant has previous experience) = 7/32 = 0.22 P( the applicant does not have previous experience) = 25/32 = 0.78 We use classic approach because the events are equal likely outcomes. 8. The president of a company has a hunch that there is a .80 probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, relative frequency, or subjective probability? Explain why. It is a subjective probability, because the probability given here assigned to an event based on subjective judgment, and experience of the president of the company. 9. The coach of a college football team thinks there is a .75 probability that the team will win the national championship this year. Is this a case of classical, relative frequency, or subjective probability? Explain why. It is a subjective probability, because the probability given here assigned to an event based on subjective judgment, and experience of the coach of the college football team. 10. A random sample of 2000 adults showed that 1120 of them have shopped at least once on the Internet. What is the (approximate) probability that a randomly selected adult has shopped on the Internet? P (a randomly selected adult has shopped on the Internet) = 1120/2000 P = 0.56 Dr. SaMeH Page 3 Stat 101 – Sheet 8 (Solutions) 11. In a group of 50 executives, 29 have a type A personality. If one executive is selected at random from this group, what is the probability that this executive has a type A personality? P (executive has a type A personality) = 29/50 =0.58 12. A multiple-choice question on a test has five answers. If Dianne chooses one answer based on “pure guess,” what is the probability that her answer is a. correct? = 1/5 = 0.2 b. wrong? = 4/5 = 0.8 Do these two probabilities add up to 1.0? If yes, why? Because each of the two answers for the five questions has the same probability of being selected. 13.Suppose you want to find the (approximate) probability that a randomly selected family from Los Angeles earns more than $125,000 a year. How would you find this probability? What procedure would you use? Explain briefly. Use relative frequency approach You are required to explain why? Dr. SaMeH Page 4