Probability and Statistics Mean Random Variable

In the table above, what are P(A and E) and P(C|E)?

For the tree diagram pictured above, what is P(B|X)?

It turns out that 25 seniors at Fashionable High School took both the AP Statistics exam and the AP Spanish Language exam. The mean score on the Statistics exam for the 25 seniors was 2.4 with a standard deviation of 0.6, and the mean score on the Spanish Language exam was 2.65 with a standard deviation of 0.55. We want to combine the scores into a single score. What are the correct mean and standard deviation of the combined scores?

The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follows: White: 46%, Latino: 32%, Asian: 11%, Black: 7%, and Other: 4%. Assuming that these are mutually exclusive categories (this is not a realistic assumption), what is the probability that a randomly selected person from the state of California is of Asian or Latino descent?

The following are the probability distributions for two random variables, X and Y: If X and Y are independent, what is P(X = 5 and Y = 4)?

The following table gives the probabilities of various outcomes for a gambling game.

What is the player’s expected return on a bet of $1?

You own an unusual die. Three faces are marked with the letter “X,” two faces with the letter “Y,” and one face with the letter “Z.” What is the probability that at least one of the first two rolls is a “Y”?

You roll two six-sided dice. What is the probability that the sum is 6 given that one die shows a 4?

Find μX and σX for the following discrete probability distribution:

Consider a set of 9000 scores on a national test that is known to be approximately normally distributed with a mean of 500 and a standard deviation of 90.

(a) What is the probability that a randomly selected student has a score greater than 600?

(b) How many scores are there between 450 and 600?