A committee is to consist of a chair, three hagglers, and four do-nothings. The committee is formed by choosing randomly from a pool of 10 people and assigning them to the various "jobs."
(a) How many different committees are possible?
(b) Norman is eager to be the chair of the committee. What is the probability that he will get his wish? (Round your answer to two decimal places.)
(c) Norman's girlfriend Norma is less ambitious and would be happy to hold any position on the committee provided that Norman is also selected as a committee member. What is the probability that she will get her wish and serve on the committee? (Round your answer to two decimal places.)
(d) Norma does not get along with Oona (who is also in the pool of prospective members) and would be most unhappy if Oona were to chair the committee. Find the probability that all Norma's wishes will be fulfilled: She and Norman are on the committee, and it is not chaired by Oona. (Round your answer to two decimal places.)
At the Stop 'n Go tune-up and brake shop, the manager has found that an SUV will require a tune-up with a probability of 0.6, a brake job with a probability of 0.1 and
both with a probability of 0.02. What is the probability that an SUV requires neither type of repair?
By how many newtons do you increase the weight of your car when you fill up your 11.5 gal gas tank with gasoline? A gallons is equal to 3.788L, and the density of gasoline is 737kg/m³.