{10.2}   Suppose that events E and F are​ independent, ​P(E)=0.7​, and ​P(F)=0.6. What is the P(E and F)​?

The E be the event that a new car requires engine work under warranty and let T be the event that the car requires transmission work under warranty. Suppose the P(E) = 0.05, P(T) = 0.06, P(E and T) = 0.03. Find the probability that the car needs no work on the engine.

Please answer number 8. Make sure to show work! Thanks!!

Suppose the probability that a male develops some form of cancer in his lifetime is 0.4573. Suppose the probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51, and that this probability is independent of the probability that a male will develop cancer in his lifetime. • C = a man develops cancer in his lifetime• F = a man has at least one false positive Part (a) Construct a tree diagram of the situation.     P(C) =  P(F | C) =  P(F | C' )    If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not. -You cannot assume the man has cancer because there is not enough information given. -You cannot assume the man has cancer because there is a 51% chance that the test is false.     -You cannot assume the man has cancer because both the probability of developing cancer in his lifetime and the probability of…

1. Answer the following questions using the probability tree below: .2 .3 X .3 .8 a Y (a) What is the value of z? (b) What is the probability of X occurring? (c) What is Pr[Xa] (Note: Pr[Xa] = Pr[X and a].) (d) What is Pr[X_or a]? (e) What is Pr[a|X]? (f) What is Pr[c]?

A bag contains 9 Blue balls, 5 Red balls, and 7 Green balls. Two balls are going to be drawn from the bag (one at a time) and then put to the side (they are not returned to the bag). Let event B = blue ball chosen, R = Red ball chosen, and G = Green ball chosen. What is P(BR)? Write an answer to 4 decimal places. Ih

A state legislator wants to determine whether her performance rating (0-100) has changed from last year to this year. The following table shows the legislator's performance rating from the same 8 randomly selected votes for last year and this year. At σ = 0.01, is there enough evidence to conclude that the legislator's performance rating has changed?

Let A and B be independent events with P(A) = 0.47 and P(B) = 0.33 . Find P(A and B).

Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like?         a. The area in the right tail of the standard normal curve.   b. The area not including the right tail of the standard normal curve.…

For each day that Sasha travels to work, the probability that she will experience a delay due to traffic is 0.2. Eachday can be considered independent of the other days. In the question,  What is the probability that Sasha’s first delay due to traffic will occur after the fifth day of work travel? Why is it that the answer is 0.32768? How did we get the solution?