The proportion of people in a given community who have a certain disease is 0.01. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.95. If a person does not have the disease, the probability that the test will produce a positive signal is 0.02.

a.Given that the test is positive, what is the probability that the person has the disease?

b.Given that the test is negative, what is the probability that the person does not have the disease?

c.For many medical tests, it is standard procedure to repeat the test when a positive signal is given. Assume that repeated medical tests are independent. What is the probability that the person has the disease given that two independent tests are positive?

A crossing track was constructed over a water channel with a total length of 1700 m and width of 40 m. If you know that the maximum flow that can be carried by the water channel is 400 m3/s over a 25-year storm event. Calculate:

a. The probability that the crossing track will flood next year.

b. The probability that the crossing track will flood at least once in the next 12 years.

c. The probability that the crossing track will not flood in the next 12 years.

d. The probability that the crossing track will flood exactly 5 times in the next 12 years. e. The probability that the crossing track will flood at least three times in the next 250 years.

1. In San Francisco, 30% of workers take public transportation daily. In a sample of 10 workers,
   1. Clearly state what the random variable in this problem is?
   2. What is an appropriate distribution to be used for this problem and why?
   3. What is the probability that exactly three workers take public transportation daily?
   4. What is the probability that NONE of workers take public transportation daily?
   5. What is the probability that more than five workers take public transportation daily?
   6. What is the probability that less than seven workers take public transportation daily?
   7. What is the probability at least two but no more than eight workers take public transportation daily?

show how to do in excel please

Suppose that 51% of all adults regularly consume coffee, 63% regularly consume carbonated soda, and 72% regularly consume coffee OR carbonated soda.

Note: Your answer must have both side of probability definition . Hint P (?) =?

(a) (5 points) What is the probability that a randomly selected adult regularly consumes both coffee and soda? Draw Venn diagram and label (with probability) each portion of the diagram to answer this question.

(b) (2 points) What is the probability that a randomly selected adult regularly consume at most one of these two products?

(c) (2 points) What is the probability that a randomly selected adult consume none these two products?

Suppose we have assigned grades for the 11 students in our data: Grade A for students who scored ≥ 90; B for students who scored ≥ 80 and < 90; C for students who scored ≥ 70 and < 80; D for students who scored ≥ 60 and < 70; F for students who scored < 60.
Following the above grade scheme, we observe that we have
8 students who received grade A,
2 student received grade B,
0 students received grade C,
0 students received grade D and
1 student received grade F. Using this, please answer the following questions:

PART 1 For each of the following statements, indicate symbolically the information given in the statement or the question. If you are not given a numeric value, then end your equation with a “?” Example: Given that the registered voter is an independent(I), the probability the voter opposes(O) the proposition is 0.80. Answer: P(O│I) = 0.80 1. The probability that a driver will be exceeding the speed limit (E) is 0.15. 2. When a new machine is functioning properly (F), only 3% of items produced are defective (D). 3. What is the probability that a randomly selected driver on the freeway will exceed the speed limit (E) and be stopped by the highway patrol (S)? 4. If a driver is exceeding the speed limit on the freeway (E), the probability that the driver will be stopped by the highway patrol (S) is 0.01. 5. If a driver is not exceeding the speed limit on the freeway (EC), the probability that the driver will be stopped by the highway patrol(S) is 0.001. 6. What is the probability that a driver on the freeway was neither stopped by the highway patrol (S) nor was exceeding the speed limit (E)? 7. What is the probability that a driver on the freeway who has been stopped by the highway patrol (S) was exceeding the speed limit (E)? 8. Past experience indicates that for 75% of successful bids (S) the agency requested additional information (I). 9. If a student goes to school full time (F), the probability that school quality is the first reason for choosing a school (Q) is 0.473. 10. What is the probability that a randomly chosen student goes to school full time (F) or has school quality as the first reason for choosing a school (Q)? 11. The Dallas IRS auditing staff believes that the probability of finding a fraudulent return (F) given that the return contains deductions for contributions exceeding the IRS standard (E) is 0.20.  

Suppose 16 coins are tossed. Find the probability of getting the following result using the binomial probability formula and the normal curve approximation.

Exactly 6 heads.

Binomial probability =

​(Round to 4 decimal​ places.)

Normal curve approximation almost =

​(Round to 4 decimal​ places.)

From the first test, 65% of the class received an ‘A’ grade.

1. Sampling 5 students, what is the probability that 1 will have an A?

2. Sampling 6 students, what is the probability that all 6 will have an A?

3. Sampling 12 students, what is the probability that at LEAST 9 will have an A?

Consider the probability that greater than 8888 out of 151151 people have not been in a car accident. Assume the probability that a given person has not been in a car accident is 57%57%.

Approximate the probability using the normal distribution. Round your answer to four decimal places.

Here is the probability model for the blood type of a randomly chosen person in the United States.

What is the probability that a randomly chosen American does not have type O blood?
% Round to the nearest 0.01%