We are purchasing a new TV!

Let A be the event that the TV was manufactured in the U.S., B be the event that the TV has Wifi, and C the event that the customer purchased an extended warranty.

Relevant probabilities are:

P(A) = 0.75

P(B|A) = 0.9

P(B|A′) = 0.8

P(C|A ∩ B) = 0.8

P(C|A ∩ B′) = 0.6

P(C|A′ ∩ B) = 0.7

P(C|A′ ∩ B′) = 0.3

a. What is the probability that the TV was manufactured in the US, with Wifi, and the customer purchased an extended warranty?

b. What is the probability that the TV does NOT have Wifi or the customer did NOT purchase an extended warranty?

c. What is the probability that the customer purchased an extended warranty?

d. What is the probability that the TV does NOT have Wifi given that it was not manufactured in the US?

5. Suppose the installation time in hours for a software on a laptop has probability density function f(x) =4/3(1−x^3), 0 ≤ x ≤ 1.

(a) Find the probability that the software takes between 0.3 and 0.5 hours to be installed on your laptop.

(b) Let X1,...,X30 be the installation times of the software on 30 different laptops. Assume the installation times are independent. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.

(c) Instead of taking a sample of 30 laptops as in the previous question, you take a sample of 60 laptops. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.

In an​ experiment, college students were given either four quarters or a​ $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts​ (a) through​ (c) below. Purchased Gum Kept the Money Students Given Four Quarters 27 13 Students Given a​ $1 Bill 18 26 a. Find the probability of randomly selecting a student who spent the​ money, given that the student was given four quarters. The probability is nothing . ​(Round to three decimal places as​ needed.) b. Find the probability of randomly selecting a student who kept the​ money, given that the student was given four quarters. The probability is nothing . ​(Round to three decimal places as​ needed.) c. What do the preceding results​ suggest?

A local business promotes oil changes that last on the average of 45 minutes with a standard deviation of 10 minutes.  If the process of changing oil follows a normal distribution, answer the following:

1. What is the probability an oil change takes less than 40 minutes?
2. What is the probability that the oil change takes between 35 and 55 minutes?
3. What is the probability that an oil change takes less than 49 minutes.
4. What is the probability that an oil change takes between 42 and 52 minutes.
5. The company wants to keep its customers.  So for the longest 5% of oil changes, the owner wants to give the customer 50% off his next visit.  How long would it take for the oil change if the customer qualifies for the discount.

Consider three choices A, B, C. Choice A gives $30 with probability 1/2 and $70 with probability 1/2. Choice B gives $50 with certainty. Choice C gives $40 with probability 1/2 and $70 with probability 1/2.
(a) [2 points] For a risk averse individual, determine if the individual (i) prefers A over B, or
(ii) prefers B over A, or (iii) more information on the individual's risk attitude is needed to compare A,B for the individual.
(b) [4 points] Carry out the same comparison as in (a) between choices (A,C) and (B,C) for a risk averse individual.
(c) [3 points] How do the conclusions in (a)-(b) change when the individual is risk neutral instead of risk averse?

Suppose your friend is always between 11 and 16 minutes late. Within this range, it's equally likely that they will appear at any time. Use this information to answer the following.

A)What type of distribution best fits your friend's arrival pattern?

B)What is the probability that your friend will be between 13 and 15 minutes late? Express your answer as a simplified fraction.

C)What is the probability that your friend will be between 12 and 15 minutes late? Express your answer as a simplified fraction.

D) What is the probability that your friend will be more than 15 minutes late? Express your answer as a simplified fraction.

E)What is the probability your friend is exactly 11 minutes late?

3. The television show Cold Case has a 15 share, meaning that while it is being broadcast, 15% of the TV sets in use are tuned to Cold Case (based on the Nielson Media Research). A group that consists of 12 randomly selected households (each with one TV set) is taken. This is a binomial distribution.

1. For such a group of 12, determine the probability that exactly four TV sets are tuned into cold case.
2. For such a group of 12, determine the probability that 4 or more TV sets are tuned into Cold Case.
3. For such a group of 12, determine the probability that at most 4 TV sets are tuned into Cold Case.
4. For such a group of 12, determine the probability that no TV sets are tuned into Cold Case. Is this situation unusual? Why or why not?
5. Determine the mean and standard deviation.

Draw a diagram of the normal distribution for all questions being asked.

40% of the population has type A blood.

• If 8 people are selected at random, what is the probability that four or less of them have type A blood.
• If 80 donors come to give blood one day, what is the probability that 40 or less of them have Type A blood (using the normal approximation)? Explain why this is higher or lower than the answer in part (a).
• If 10 people give blood one day, what is the probability that more than 5 of them are Type A?
• If 100 people come to give blood, what is the probability that more than 50 the donors is of Type A? Explain why this answer is higher or lower than the answer in part (c).

Of all failures of a certain type of computer hard drive, it is determined that in 15% of them only the sector containing the file allocation table is damaged (F), in 65% of them only nonessential sectors are damaged (S), and in 20% of the case , both the allocation sector and one or more essential sectors are damaged.A failed drive is selected at random and examined.

a)Represent this information in Venn Diagram

b)Given that the drive has damaged file allocation sector.

1) what is the probability that some nonessential sectors are damaged as well?

2)what is the probability that no nonessential sectors are damaged?

c)Given that the drive has damaged nonessential sector.

1)what is the probability that file allocation sector is damaged as well?

2)what is the probability that allocation sector is not damaged?

the probability that a randomly selected 3 ​-year-old male garter snake will live to be 4 years old is 0.98191 .

​(a) what is the probability that two randomly selected 3 ​-year-old male garter snake s will live to be 4 years​ old? ​

(b) what is the probability that five randomly selected 3 ​-year-old male garter snake s will live to be 4 years​ old?

​(c) what is the probability that at least one of five randomly selected 3 ​-year-old male garter snake s will not live to be 4 years​ old? would it be unusual if at least one of five randomly selected 3 ​-year-old male garter snake s did not live to be 4 years​ old?