5. Determine the probabilities of the following outcomes and events: (a) Tossing two coins and getting either one or two heads. (b) Randomly selecting a three-child family with exactly two girls.
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- 5. Help please6. An oil exploration company is planning to drill for oil in a new location. Their geologists give them the following probabilities. There is a 10 % probability of making $20,000,000 on this project. There is a 30% probability .of making $12,000,000 on this project There is a 40% probability of making $5,000,000 on this project. Otherwise, they lose their $8,000,000 a) Make up a probability distribution for this drilling project. b) What is the expected value of this drilling project? c) If you owned the company, would you drill? Explain your answer briefly.1.involving the rental cars with navigation systems. Assume that the car lot contains 35 percent Lincolns, 30 percent Corvettes, and 35 percent BMWs. Of the Lincolns, 50 percent have navigation systems, 30 percent of the Corvettes have navigation systems, and 40 percent of the BMWs have navigation systems. You are assigned a car at random. If the car has a navigation system, what is the probability that it is not a Lincoln? 2. Three people are selected for a committee from 4 Democrats and 3 Republicans. What is the probability the committee contains both Democrats and Republicans given that it contains at least two Democrats?
- In three independent flips of a coin where there is a 63% chance of flipping a tail, let A denote {first flip is a tail}, B denote {second flip is a tail}, C denote {first two flips are tails}, and D denote {three tails on the first three flips}. Find the probabilities of A, B, C, and D, and determine which, if any, pairs of these events are independent. P(A)= (Round to two decimal places as needed.) P(B)= (Round to two decimal places as needed.) P(C)= (Round to four decimal places as needed.) P(D)= (Round to four decimal places as needed.) Which of these pairs of events are independent? A. Events A and B because P(A and B)=P(A)•P(B). B. Events A and C because P(A and C)=P(A)•P(C). C. None of the pairs of events are independent. D. Events C and D because P(C and D)=P(C)•P(D)1. The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer? (PERCENTAGE FORMAT) 2. At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in the university is a male in the business faculty? b. What is the probability that a student selected at random in the university is male or is in the business faculty? c. What percentage of males are in the business faculty? (PERCENTAGE FORMAT)6. In a game of chance, a contestant must choose a number from one of three categories. Correct number choices in Category A are worth $1500, but there is a penalty of $1000 for each incorrect choice. Correct number choices in Category B are worth $1000, with a $500 penalty for each incorrect choice. Correct number choices in Category C are worth $500, with no penalty for an incorrect choice. The probability of choosing correctly is 0.05 for Category A, 0.15 for Category B, and 0.25 for Category C. Which category has the highest expected value? Find the exnected yalue for each of the unequal spinners shown. Inpors chown
- A shop keeper sells three models of televisions A, B and C.Sale of model A is 40% of which 3% are with stereo.Sale of model B is 40% of which 7% are with stereo.Sale of model C is 20% of which 9% are with stereo.What is the probability that a randomly sold television is with stereo?The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 36% of all purchasers request A, 47% request B, 69% request C, 54% request A or B, 75% request A or C, 76% request B or C, and 78% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.Audrey has the following t-shirts in her dresser drawer. She will randomly choose one t-shirt. Then she will replace it and choose a second t-shirt. What is the probability that she chooses a polka dot shirt and then a striped shirt? • 5 striped t-shirts • 6 solid t-shirts • 2 floral t-shirts • 2 polka dot t-shirts Responses
- 15.An automobile company manufactures parts fo car out of which10% are defective. Find the probabilities that among 18 such partsrandomely chosen(a) all are defective.(b) at least 16 are defective.(c) at most 14 are defective.(d) exactly 10 are defective.The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 53% of all purchasers request A, 60% request B, 76% request C, 70% request A or B, 91% request A or C, 86% request B or C, and 93% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.
