Unit 3!
3. Statistical Literacy What is the probability of (a) an event A that is certain to occur? (b) an event B that is impossible?13. Critical Thinking Consider the following events for a driver selected at ran- dom from the general population: A = driver is under 25 years old B = driver has received a speeding ticket Translate each of the following phrases into symbols. (a) The probability the driver has received a speeding ticket and is under 25 years old (b) The probability a driver who is under 25 years old has received a speed- ing ticket (c) The probability a driver who has received a speeding ticket is 25 years old or older (d) The probability the driver is under 25 years old or has received a speeding ticket (e) The probability the driver has not received a speeding ticket or is under 25 years oldI on the first toss, are you guaranteed to get tails on the second toss? Explain. 14. | Critical Thinking (a) Explain why -0.41 cannot be the probability of some event. (b) Explain why 1.21 cannot be the probability of some event. (c) Explain why 120% cannot be the probability of some event. (d) Can the number 0.56 be the probability of an event? Explain.23. Business: Customers John runs a computer software store. Yesterday he counted 127 people who walked by his store, 58 of whom came into the store. Of the 58, only 25 bought something in the store. (a) Estimate the probability that a person who walks by the store will enter the store. (b) Estimate the probability that a person who walks into the store will buy something. (c) Estimate the probability that a person who walks by the store will come in and buy something. (d) Estimate the probability that a person who comes into the store will buy nothing.Section 5.2 Some Probability Rules-Compound Events 217 Utah. The park is famous for its beautiful desert landscape and its many natu- ral sandstone arches. Park Ranger Edward McCarrick started an inventory (not yet complete) of natural arches within the park that have an opening of at least 3 feet. The following table is based on information taken from the book Canyon Country Arches and Bridges by F. A. Barnes. The height of the arch opening is rounded to the nearest foot. Height of arch, feet 3-9 10-29 30-49 50-74 75 and higher Number of arches in park 111 96 30 33 18 For an arch chosen at random in Arches National Park, use the preceding information to estimate the probability that the height of the arch opening is (a) 3 to 9 feet tall (b) 30 feet or taller (c) 3 to 49 feet tall (d) 10 to 74 feet tall (e) 75 feet or taller5. | Basic Computation: Multiplication Rule Given P(A) = 0.2 and P(B) = 0.4: (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B). 6. Basic Computation: Multiplication Rule Given P(A) = 0.7 and P(B) = 0.8: (a) If A and B, are independent events, compute P(A and B). (b) If P(BIA) = 0.9, compute P(A and B). 7. Basic Computations: Rules of Probability Given P(A) = 0.2, P(B) = 0.5, P(A | B) = 0.3: (a) Compute P(A and B). (b) Compute P(A or B).18. General: Roll a Die (a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? (b) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1? Should they add up to 1? Explain. (c) What is the probability of getting a number less than 5 on a single throw? (d) What is the probability of getting 5 or 6 on a single throw
