Probability Examples and Explanations

A standard pair of six sided dice is rolled. What is the probability of rolling a sum greater than 3? 
 

Given P(A) = 0.92, P(B) = 0.33, and P(A or B) = 0.40, are events A and B mutually exclusive?

What is the probability that a randomly selected student is a female? *

1 point

A.11/3

B.77/12

C.55/11

D.88/15

Statistics and Probability

The joint probability distribution of two random variables X and Y is given in the following table.

1. Calculate the marginal probability distribution of X.
2. Calculate the marginal probability distribution of Y.
3. Calculate E( X ) and s.d.( X ).
4. Calculate E( Y ) and s.d.( Y )
5. Calculate cov(X, Y) and corr(X, Y).
6. Calculate the conditional probability distribution of X given Y = -1.
7. Calculate the conditional probability distribution of X given Y = 2.
8. Calculate E( X | Y = -1 ) and var( X | Y = -1 ).
9. Calculate E( X | Y = 2 ) and var( X | Y = 2 ).
10. Verify the Law of Iterated Expectations E(X)=E[E(X|Y)] by using your previous results.
11. Are X and Y independent random variables? Justify your answer based on answers to the preceding questions.

More cereal. In Exercise 37 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounces. a) Find the expected amount of cereal left in the box. b) What’s the standard deviation? c) If the weight of the remaining cereal can be described by a Normal model, what’s the probability that the box still contains more than 13 ounces?

70% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 31 owned dogs are randomly selected, find the probability that

a. Exactly 20 of them are spayed or neutered. 
b. At most 24 of them are spayed or neutered. 
c. At least 22 of them are spayed or neutered. 
d. Between 16 and 23 (including 16 and 23) of them are spayed or neutered. 

Round all answers to 4 decimal places.

You measure weekly sales. You can assume that weekly sales are normally distributed with mean 60 and standard deviation 18, and that weekly sales are independent across weeks.

What is the probability that AVERAGE WEEKLY sales over the next 4 weeks are below 66 in 4 decimal positions?

1. Random sample of size 4 are drawn from the finite population which consists of the numbers 2,3,7,8,and 10. a. What is the population mean, population variance and population standard deviation of the given data? b. What is the sampling distribution of the sample means for a sample of size 2 which can be drawn without replacement from the given population? c. What is the mean, variance and standard deviation of the samp

If two events A and B are independent and you know
that P(A) = 0.3, what is the value of P(A | B)?

Assuming that, on average, 4 out of 5 planes at Mactan International Airport arrive on schedule for a        particular time period, what is the probability that out of 8 planes, chosen at random:

        1.1) all 8 planes arrive on schedule?

        1.2) 5 arrive on schedule?

        1.3) at least 6 arrive on schedule?

Refer to the scenario and table provided below. The number of qualified voters living in the household on a randomly selected Subdivision block is described by the following probability distribution. Find the MEAN. *