In the game of poker, determine the number of ways a straight (five cards with consecutive values, such as A 2 3 4 5 or 7 8 9 10 J or 10 J Q K A, but not all of the same suit) can be picked.

Suppose that 42% of the seeds of a certain plant germinate. (a) What is the expected number of germinating seeds in a sample of 10 seeds? (b) You plant 10 seeds in one pot. What is the probability that none of the seeds will germinate? (c) You plant five pots with 10 seeds each. What is the expected number of pots with no germinating seeds? (d) You plant five pots with 10 seeds each.What is the probability that at least one pot has no germinating seeds?

Assume that $\Omega=\{1,2,3,4,5,6\},$ A = {1, 3, 5}, and B = {1, 2, 3}. Find $A \cup B$ and $A \cap B.$

Let X be uniformly distributed over (−2, 2). Use Chebyshev’s inequality to estimate $P(|X| \geq 1),$ and compare your estimate with the exact answer.

An urn contains three green and two blue balls. You remove two balls at random without replacement. Let X denote the number of green balls in your sample. Find the probability mass function describing the distribution of X.

The Muesli-Mix is a popular breakfast hangout near a campus. A typical breakfast there consists of one beverage, one bowl of cereal, and a piece of fruit. If you can choose among three different beverages, seven different cereals, and four different types of fruit, how many choices for breakfast do you have?