Consider a sample space with 3 A’s and 2 B’s. Assume that each sample point is equally likely to be selected.

(a) What is the probability that a randomly selected set of 2 items will include all B’s?

(b) What is the probability that a randomly selected set of 3 items will include all A’s? 1

(c) What is the probability that a randomly selected set of 2 items will include 1 A and 1 B?

(d) What is the probability that a randomly selected set of 3 items will include 2 A’s and 1 B?

Allele frequency is the relative frequency of a certain allele type among a certain population. Suppose that within a certain area, the allele frequency of A, B and O are 0.2, 0.1, and 0.7, respectively. Suppose that when randomly picking up a person, the first allele type is independent of the second allele type regardless of the type. Calculate the following probabilities:

• The probability for this person to have type O blood.

• The probability for this person to have type A blood.

• The probability for this person to have type B blood.

• The probability for this person to have type AB blood.

Please give a step by step solution:

The ages of a group of 50 women are approximately normally distributed with a mean of 50 years and a standard deviation of 55 years. One woman is randomly selected from the​ group, and her age is observed.

a. Find the probability that her age will fall between 56 and 59years.

b. Find the probability that her age will fall between 4747 and 51 years.

c. Find the probability that her age will be less than 35 years.

d. Find the probability that her age will exceed 41 years.

A stock sells today for $130. The price of the stock in a year is expected to be $140. The annual volatility of the stock is 30%.
a. Calculate the probability that in six years the stock will sell for more than $150.
b. Calculate the probability that in six years the stock will sell for less than $115.
c. Calculate the probability that in six years the stock will sell for a price between $120 and $160.
d. You are 85% confident the stock price in six years will be between what two values?
e. There is an 80% probability that in 6 years the stock price will exceed ___________

"You are investing $6,000 immediately in a stock that you will keep for 13 years. At the end of 13 years, the stock will be worth $16,813 with a probability of 0.48 and worth $22,785 with a probability of 0.52. When you sell the stock, you will need to pay taxes on the profit earned from selling the stock (i.e., taxes on the difference between the selling and buying prices of the stock). The tax rate will be 8% with a probability of 0.8 or 16% with a probability of 0.2. Your MARR is 4.7% What is the variance of the net present worth from investing in the stock?"

In an introductory statistics class, there are 18 male and 22 female students. Two students are randomly selected (without replacement).

(a) Find the probability that the first is female

(b) Find the probability that the first is female and the second is male.

(c) Find the probability that at least one is female

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I know that this question has to use the counting method, but i got confuse with how to start because i have to now find the probability of FIRST being a female, etc. Please provide workings with explanations alongside. Thank you in advance!

In recent years, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3 Answer parts A-D below. Round to four decimal places as needed.

1. Find the probability that a randomly selected medical student who took the test has a total score that was less than 493.

The probability that randomly selected medical student who took the test had a total score that was less than 493 is [____]

2. Find the probability that a randomly selected medical student who took the test had a total score that was between 495 and 508.

The probability that a randomly selected medical student who took the test had a total score that was between 495 and 508 is [____]

3. Find the probability that a randomly selected medical student who took the test had a total score that was more than 527.

The probability that a randomly selected medical student who took the test had a total score that was more than 527 is [______]

4. Identify any unusual events. Explain your reasoning. Choose the correct answer below.

   1. The events in parts A and B are unusual because their probabilities are less than 0.05

   2. None of the events are unusual because all the probabilities are greater than 0.05

   3. The event in part A is unusual because its probability is less than 0.05

   4. The event in part C is unusual because its probability is less than 0.05

Cabin Fever Coffee is a local coffee bar, and is striving for consistent quality in their coffee beverages served to guests. Guests often complain that their beverage is not hot enough (lukewarm) or too hot and thus leave unsatisfied. Management determines that the temperature of their brewed coffee is approximately normally distributed with a mean of 101 degrees and a standard deviation of 6 degrees. Management has also set a temperature of 99 degrees or lower to be “lukewarm” and a temperature of 110 degrees to be too hot.

(Round all probability answers to four decimals)

a) What’s the probability that a customer’s beverage is lukewarm?

b) What’s the probability that a customer’s beverage is too hot?

c) What’s the probability’s the probability a customer leaves the store unsatisfied?

d) Suppose management randomly selects 9 customers from the day. What’s the probability that at least one of them left unsatisfied?

e) From the same random sample of 9 customers in part (d), what’s the probability that at most half of them left satisfied?

f) From the same random sample of 9 customers in part (d), what’s the probability that the average temperature of the sample’s coffee beverages was less than 103 degrees?

g) From the same random sample of 9 customers in part (d), what’s the probability that the average temperature of the sample’s coffee beverages was within management’s acceptable temperature range?

Cabin Fever Coffee is a local coffee bar located in Defiance, Ohio, and is striving for consistent quality in their coffee beverages served to guests. Guests often complain that their beverage is not hot enough (lukewarm) or too hot and thus leave unsatisfied. Management determines that the temperature of their brewed coffee is approximately normally distributed with a mean of 102 degrees and a standard deviation of 5 degrees. Management has also set a temperature of 96 degrees or lower to be “lukewarm” and a temperature of 107 degrees to be too hot.

(Round all probability answers to four decimals)

a) What’s the probability that a customer’s beverage is lukewarm?

b) What’s the probability that a customer’s beverage is too hot?

c) What’s the probability’s the probability a customer leaves the store unsatisfied?

d) Suppose management randomly selects 6 customers from the day. What’s the probability that at least one of them left unsatisfied?

e) From the same random sample of 6 customers in part (d), what’s the probability that at most half of them left satisfied?

f) From the same random sample of 6 customers in part (d), what’s the probability that the average temperature of the sample’s coffee beverages was less than 103 degrees?

g) From the same random sample of 6 customers in part (d), what’s the probability that the average temperature of the sample’s coffee beverages was within management’s acceptable temperature range?