Question 1

An experiment is to flip a fair coin four times. State the sample space. Let H = the coin came up heads and T = the coin came up tails. S = { } Find the probability of getting exactly two heads. P(2 heads) = Find the probability of getting at least two heads. P(at least 2 heads) = Find the probability of getting all heads or all tails. P(all heads or all tails) =

Question 2

An experiment is rolling two fair dice and adding the numbers. State the sample space. S = Find the probability of getting a sum of 12. Round to four decimal places, if necessary. P(12) = Find the probability of getting a sum of 6. Round to four decimal places, if necessary. P(6) = Find the probability of getting a sum of 3 or sum of 5. Round to four decimal places, if necessary. P(3 or 5) = Find the probability of not getting a sum of 11. Round to four decimal places, if necessary. P(not 11) =

Question 3

Read over each scenario and determine if the problem is asking you to find an experimental probability or a theoretical probability. While playing Life Heather first twelve spins were 2, 8, 4, 8, 6, 1, 3, 2, 9, 8, 7, and 10. Based on her previous spins, what is the probability that her next spin will be a 2?

• Experimental Probability
• Theoretical Probability

While playing Life Heather notices that the spinner on the game board has ten numbers and that each number is assigned to an equally sized area on the spinner. What is the probability that her next spin will be a 2?

• Experimental Probability
• Theoretical Probability

Leo and his friend have decided that they will decide where to go eat for dinner by flippling a coin. If they flip at least three heads out of five flips, then Leo will get to choose. If they get at least three tails out of five flips, then his friend will get to choose. What is the probability that Leo will get to choose where they will eat dinner?

• Experimental Probability
• Theoretical Probability

Mara Fernanda is starting to feel like the dice she is using is not fair based on the first twenty rolls. She rolls the dice 100 times to test the dice out and rolls a 3 thirty-nine times, a 5 twenty-six times, a 4 seventeen times, a 6 twelve times, a 1 five times, 2 two times. Mara Fernanda needs to roll a 4 or a 6 to win the game on her next roll. Based on her 100 rolls what is the probability that she will win on her next roll?

• Experimental Probability
• Theoretical Probability

A standard deck of cards contains 52 cards. If 4 of the cards are queens, what is the probability that a single card selected will be a queen?

• Experimental Probability
• Theoretical Probability

Kaiden has a bag of candies. The bag contains 6 red candies, 8 blue candies, 5 brown candies, 4 green candies, and 2 yellow candies. If he pulls out two red candies and eats both of them, what is the probability that the next candy his grabs will be brown?

• Experimental Probability
• Theoretical Probability

• Amelia is a medical researcher. Upon reading through a random sample of ten thousand medical records, she discovers that 150 of the patients at the hospital contracted a particular infection during their stay. What should she conclude is the probability of an individual patient contracting that particular infection during their hospital stay?
• Experimental Probability
• Theoretical Probability

Amelia is investigating the incidence of six different childhood diseases (the common cold, flu, strep throat, ear infections, the croup, and whooping cough). If she currently has no additional information and assumes that these diseases are equilogical, what would she assume is the probability of a child with one of these six diseases having whooping cough?

• Experimental Probability
• Theoretical Probability

A poll is taken of likely voters. Of the 500 citizens who were polled, 275 of them planned to vote for Rodrigo Wilson. What is the probability that the 501th likely voter plans on voting for Rodrigo Wilson?

• Experimental Probability
• Theoretical Probability

Question 4

A card is drawn from a deck of 52 cards. What is the probability that it is a picture card (Jack, Queen, King, Ace) or a heart ?

P(picture or heart)=

Question 5

In a natural habitat, 70 deer were marked with tags and released back into the park. When the park rangers re-captured 70 deer, 5 of them were tagged. How many deer do you expect there to be in the park?

Question 6

As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King). If you select a card at random, what is the probability of getting: a) A(n) 2 of Club s? (Please enter a reduced fraction.) b) A Spade or Heart? (Please enter a reduced fraction.) c) A number smaller than 2 (counting the ace as a 1)? (Please enter a reduced fraction.)

Question 7

A bag of M&M's has 2 red, 3 green, 4 blue, and 5 yellow M&M's. Suppose you randomly select two M&M's from the bag one at a time with replacing the first M&M.

Let A = first M&M is green and B = second M&M is yellow. Find the following probabilities. (Write your answers as fractions.) a) P(A) = b) P(B | A) = c) P(A and B) =

Question 8

A bag of M&M's has 2 red, 3 green, 4 blue, and 5 yellow M&M's. Suppose you randomly select two M&M's from the bag one at a time with replacing the first M&M.

Let A = first M&M is green and B = second M&M is yellow. Find the following probabilities. (Write your answers as fractions.) a) P(A) = b) P(B | A) = c) P(A and B) =

Question 9

Based on a survey, we assume that there is a 49% chance that student has a pet. Suppose that there are 6 students sitting at a table.

Find the probability of each of these events. Give each probability as a percentage rounded to two decimal places.

(a) What is the probability that all 6 students have a pet? %

(b) What is the probability that none of the 6 students have a pet? %

(c) What is the probability that at least one of the 6 students have a pet?

Question 10 A bag of M&M's has 4 red, 5 green, 3 blue, and 2 yellow M&M's. Suppose you randomly select two M&M's from the bag one at a time without replacing the first M&M.

Let A = first M&M is green and B = second M&M is red. Find the following probabilities. (Write your answers as fractions.) a) P(A) = b) P(B | A) = c) P(A and B) =

Question 11 Giving a test to a group of students, the grades and gender are summarized below

A B C TOTAL

Male 34 39 37 110

female 20 18 11 49

Total 54 57 48 159

If one student is chosen at random, Find the probability that the student got a 'C' GIVEN they are female.

Question 12

If one registered voter is chosen at random,

A B C Total

Male 34 39 37 110

Female 20 18 11 49

Total 54 57 48 159

Find the probability that the registered voter was female GIVEN they were registered as a 'Independent'. Write your answer as a decimal rounded to three decimal places.

Question 13

A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected:

Age Number of Customers

<20 54

20-29 55

30-39 64

40-49 61

50-59 69

>60 62

One customer is chosen at random for a prize giveaway. Please enter reduced fractions What is the probability that the customer is at least 40 but no older than 60? What is the probability that the customer is at least 50? What is the probability that the customer is either at least 50 or younger than 20?

Please, answer the questions sequentially. Thanks.