Probability and Statistics: Counting and Basic Probability

In a 50-person race, how many ways can you award gold, silver, and bronze where the order is important?

Determine how many permutations and combinations exist for the letters A, B, and C, where order matters for permutations and does not matter for combinations.

Given $n = 3$ and $r = 2$, calculate the number of permutations and combinations using the formulas for permutations and combinations.

Calculate the probability of getting two heads in a row when tossing a coin two times.

Calculate the probability of getting ten heads in a row when tossing a coin ten times.

Calculate the probability of getting a head on the first, a head on the second, and a tail on the third toss of a coin.

Calculate the probability of not getting four heads when tossing a coin four times.

Calculate the probability of getting two ones in two rolls of a die.

Calculate the probability of getting a 1 or 2 on the first roll of a die and a 6 on the second roll.

A bag contains 5 red, 2 blue, and 3 green balls. If you take one out, look at it, put it back, and then take another one out, what is the probability of getting one red and one green ball in any order?

A jar contains 3 red, 5 yellow, and 8 orange jelly beans. If you take one out and eat it, what is the probability of getting one yellow and one orange jelly bean in any order?

What is the probability of rolling an eight with the sum of two dice?

What is the probability that the card matches the sum of the dice in a game where you roll two dice and pick a card at random? An ace equals 1, a jack equals 11, a queen equals 12, and a king equals 13.

If I flip the same coin two times, what would be the probability of getting heads twice?

If a coin is tossed 2 times, find the probability of getting at least one tail.

If we flip two coins, what is the probability of not getting two tails?

Calculate the probability of flipping a tails when flipping a coin.

John needs to decide on his type of shirt, pants, and shoes. How many total choices does he have, and what is the probability of his unique outfit?

Jenny has a bag with seven blue sweets and three red sweets in it. She picks a sweet at random from the bag, replaces it, and then picks again at random. Draw a tree diagram to represent this situation and use it to calculate the probabilities that she picks:

a) two red sweets,

b) no red sweets,

c) at least one blue sweet,

d) one sweet of each color.