A new law is favored by 90% of voters. Suppose 8 voters are randomly selected. a) Find the probability of getting 6 voters in favor of the new law. W) Find the probabi...
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- At a certain state court the jury will convict a defendant if at least 8 out of 12 jurors support a “guilty” verdict. The jurors determined their verdict independently from each other. The probability that each juror will get the “right” decision is 0.8 (which means to convict when the defendant commit the crime and to acquit when he didn’t). a) Find the probability of convicting an innocent person.b) Find the probability of acquits a guilty person.c) Assume that 25% of the defendants in the state are innocent. In a certain year 200 people put on trial. What is the expected value and variance of the number of cases in which juries got the right decision?Suppose that the Student Representative Council (SRC) consists of 23 people (9 men and 14 women). From this five people are.randomly chosen to attend.a special group, meeting. Calculate the probability that: a majority of men and at least 1 woman are selected to attend the meeting.Assume that there are 16 frozen dinners: 9 pasta, 3 chicken, and 4 seafood dinners. The student selects 5 of them. What is the probability that at least 2 of the dinners selected are pasta dinners?
- A club with 12 female members and 11 male members is electing a president and v.p. How many election outcomes are possible? Assuming each outcome is equally likely, find the probability that: a. Both officers are male. b. The president is female. c. The two officers are of different genders.Assume there is a national lottery and the winning ticket is worth $10 million. One winning ticket will be selected. If there are 225 million tickets sold, what is the chance that a buyer of one ticket will have the winning ticket?Please show your solution in step by step process.
- Nine people apply for three jobs. Five of them are women, four of them are men. 1. If three people selected at random, what is a probability that all three are woman?(Give your answer as a fraction, you do not need to simplify) 2.lf three people selected at random, what is a probability that only one is woman?(Give your answer as a fraction, you do not need to simplify) 3. If three people selected at random, what is a probability that at least two are men?(Give your answer as a fraction, you do not need to simplify) 4.lf three people selected at random, what is a probability that at most one is a man?(Give your answer as a fraction, you do not need to simplify)Two balanced dice are thrown, one red and one black. What is the probability that the red die comes up 1, given that the a. black die comes up 3? b. sum of the dice is 4? c. sum of the dice is 9?A student must take a multiple-choice exam with only oneanswer, the exam consists of 20 questions with 4 answer options eachOne, suppose the student does not prepare for the test and answers therandom.a. Find the probability that the student will win the test.B. How many questions are you expected to answer to get the fifthcorrect answer.
- On a shelf there are 60 novels and 20 poetry books. Person Achooses a book at random off the shelf and leaves with it. Shortly after, Person Bchooses another book at random. Calculate:a. The probability that the book selected by Person B is a novel?b. If it is known that Person B chose a novel: what is the probability that thebook selected by Person A was a poetry book?On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process