Probability and Statistics: Counting and Basic Probability

Find the probability of rolling a 1 exactly twice in four rolls of a fair six-sided die.

In a game of roulette, spin the wheel three times and determine the probabilities of the ball landing in an even pocket zero, one, two, or three times.

In a game of roulette, spin the wheel three times and determine the probabilities of the ball landing in an even pocket zero, one, two, or three times.

If one of these 523 cases is randomly selected, what is the probability the person was female?

I have three pants and four shirts. How many different outfits can I wear?

Using the counting principle, calculate the number of different outfits if I have four shirts, four pants, and four shoes.

Calculate the total number of possible solutions for a lock with 10 different numbers and five slots using the counting principle.

Create a computer password using the 26 letters of the alphabet, where each letter can be used only once, and the password is four spaces long. How many different passwords are possible?

Form a five-digit number on a given keypad for an apartment entrance. Calculate the number of possible codes if repeats are allowed.

Calculate the number of possible five-digit codes on a keypad if no repeats are allowed.

Determine the number of possible five-digit codes with at least one repeat on the keypad.

Calculate the number of possible codes if the five-digit number has to be odd.

Find the probability of rolling a prime number and flipping heads.

Find the probability of choosing both Jokers without replacing the first Joker before the second selection.

Find the probability of choosing a Heart, putting it back, and then choosing a Spade.

What’s the probability of rolling snake eyes?

What’s the probability of flipping heads three times in a row?

Suppose that we want to find out the probability of first drawing a green marble and then a blue marble out of a bag of 12 marbles. There are three green marbles, four blue marbles, and five red marbles. Find the probability using the multiplication rule of probability.

How many ways can you arrange 5 books on a shelf where the order is important?

How many ways can you pick 2 co-captains on a team of 20 where the order does not matter?