High school probability Uncovered: Discover the Secrets with Plainmath's Expert Help

Two fair dice are rolled. Find the joint probability mass function of X and Y when (a) X is the largest value obtained on any die and Y is the sum of the values; (b) X is the value on the first die and Y is the larger of the two values; (c) X is the smallest and Y is the largest value obtained on the dice.

a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.
i. Define the variable of interest for this scenario.
ii. What probability distribution do you think best describes the situation? Why?
iii. Calculate the probability that exactly 9 will buy the product.

It is conjectured that an impurity exists in 30% of all drinking wells in a certain rural community. In order to gain some insight on this problem, it is determined that some tests should be made. It is too expensive to test all of the many wells in the area, so 10 were randomly selected for testing. a. Using the binomial distribution, what is the probability that exactly three wells have the impurity assuming that the conjecture is correct? b. What is the probability that more than three wells are impure?

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with ${\displaystyle P\left(A\right)=0.4,P\left(B\right)=0.2,\text{and}P\left(C\right)=0.4}$.
(a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card?
$$\begin{array}{|cc|}\hline mean& customers\\ variance& customer{s}^2\\ \hline\end{array}$$
Explain your reasoning.
Because we are interested in whether or not a debit card was used, we can use the binomial distribution. ${\displaystyle X=}$ the probability that a customer used a debit card.Because we are interested in whether or not a debit card was used, we can use the binomial distribution. ${\displaystyle X=}$ the number of customers who use a debit card. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. ${\displaystyle X=}$ the number of customers at the gas station.
(b) Answer part (a) for the number among the 100 who dont

Beth is taking an eleven​-question ​multiple-choice test for which each question has three answer​ choices, only one of which is correct. Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or​ 2, the second if the die shows 3 or​ 4, and the third if the die shows 5 or 6. Find the probability of the stated event.
exactly
four
correct answers

What does exclamation an point mean?

Tell, what is the factorial of 10?

The probability that a student passes the Probability and Statistics exam is 0.7.
(i)Find the probability that a given student will pass the Probability and Statistics exam after the third try.
(ii)Find the probability that the third student who fails the Probability and Statistics exam is found after the fifth student in a class of 9 students?
(iii)Find the probability that at most 3 students will pass the Probability and Statistics exam in a class of 7 students.

An oil drilling company ventures into various locations, and its success or failure is independent from one location to another. Suppose the probability of a success at any specific location is 0.30. What is the probability that a driller drills 10 locations and finds 1 success? The driller feels that he will go bankrupt if he drills 10 times before the first success occurs. What are the driller's prospects for bankruptcy? i. ii.

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected.
If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that meets the contract requirements will end up being 100 percent inspected is approximately...
A) .086
B) .41
C) .68
D) There is insufficient information to answer

In a 10-question true/false test, what is the probability of guessing correctly on questions 1 through 4 exactly 2 times?

Suppose that you are rolling a six sided dice. Let A-get a 3 What is P(A)?
a. 4/6
b. 5/6
c. 1/6
d. 3/6

Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter ${\displaystyle \frac{1}{20}}$. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it? Repeat under the assumption that the lifetime mileage of the car is not exponentially distributed, but rather is (in thousands of miles) uniformly distributed over (0,40).

An insurance company found that 25% of all insurance policies are terminated before their maturity date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a Binomial experiment.
Required:
What is the probability that at most eight policies are not terminated before maturity?

Consider a binomial experiment with ${\displaystyle n=20\text{and}p=.70}$.
1. Compute f (12).
2. Compute f (16).
3. Compute ${\displaystyle P(x\ge 16)}$.

Suppose we have two weighted coins, one of which comes up heads with probability 0.3, and the other of which comes up heads with probability 0.8. Unfortunately, the coins are otherwise identical, and we have lost track of which is which. Suppose we flip a randomly chosen coin 14 times and let N be the random variable giving the number of heads seen. If in the first 3 flips we see 2 heads, what is the conditional expected number of heads in the 14 flips?
${\displaystyle E\left[N\mid 2\text{of first 3 are H}\right]=?}$

Approximately 80,000 marriages took place in the state of New York last year. Estimate the probability that, for at least one of these couples, (a) both partners were born on April 30; (b) both partners celebrated their birthday on the same day of the year. State your assumptions.