P(B'/A) = 1 − P(B/A)
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Prove the following
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- The probability that a certain machine turns out a defective item is 0.05. Find theprobability that in a run of 30 items, the machine produces exactly 3 defective items. (Assumeindependence between items.)Use Baye's Theorem to solve this problem, A paper bag contains two red balls and one blue ball. A plastic bag contains three blue balls and one red ball. A coin is tossed. If it falls heads up, the paper bag is selected and a ball is drawn. If the coin falls tails up, the plastic bag is selected and a ball is drawn. If a red ball is selected, what is the probability that it came from the paper bag? O A. 1 В. 3 C. 8 8 11 1/3O None of these Question * 70% of a certaim species of tomato live after transplanting from pot to garden. Najib transplants 3 of these tomato plants. Assume that the plants live independently of each other. Let X equals the number of tomato plants that live. What is the probability that exactly 1 of the 3 tomato plants live? O0.441 0.2646 0.189 None of these Question
- Which of the following events is not a classical probability? a. The probability of repairing a washing machine during a six-year period is 0.10. b. The probability of rolling a die and getting 6 is 1/6. c. The probability of choosing six numbers from 1 to 40 that match the six numbers drawn by a state lottery is 1/3,838,380. d. The probability of pulling a spade king from a deck of cards is 1/52.A random number generator produces sequences of independent digits, each of which is as likely to be any digit form of 0 to 9 as any other. If X denotes any single digit, find the mean or expected value of the probability distribution.A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.050.05. On visiting a holiday resort for seniors, he sells 1010 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 1010 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places.Part a)What is the expected number of policies that will pay out before the insured parties have reached age 61?Part b)What is the variance of the number of policies that will pay out before the insured parties have reached age 61?Part c)What is the probability that at least two policies will pay out before the insured parties have reached age 61?
- In a certain insurance has 20 holders. The ages of these policy holders are as follows: One is 16 years old, four are 18, nine are 19, three are 20, two are 21, and one is 30. Let X= age of any policy holder (randomly selected). Find the probability mass function of age.A surprising result that appears in many Elementary discussions on probability is called the birthday problem. The question simply stated is that if we poll a certain number of people, what is the probability that at least two of those people were born on the same day of the year? To solve this problem, use the formula for computing the probability of a complement of a event. It is clear that P(duplication of some birthdays)=1-P(n I duplications). Assume that there are 4 people. Find the probability that at least 2 of the 4 people were born on the same day of the year. Do not consider February 29th in leap year when finding the probability.K In a certain state, it has been shown that only 54% of the high school graduates who are capable of college work actually enroll in college. Find the probability that, among 10 capable high school graduates in this state, 5 to 7 inclusive will enroll in college. The probability that, among 10 capable high school graduates in this state, from 5 through 7 will enroll in college is (Round to three decimal places as needed.) ☐
