AP Statistics

Probability Worksheet 1

  1. For each of the following, list the sample space and tell whether you think the events are equally likely.
  2. Roll two dice; record the sum of the numbers
  1. A family has 3 children; record the genders in order of birth
  1. Toss four coins; record the number of tails
  1. Toss a coin 10 times; record the longest run of heads.
  1. Real estate ads suggest that 23% of homes for sale have fireplaces, 65% have a second bathroom, and 13% have both features. What is the probability that a home for sale has

VENN DIAGRAM:

  1. a second bathroom and a fireplace?
  1. neither a second bathroom nor a fireplace?
  1. a second bathroom but no fireplace?
  1. a second bathroom given that the house has a fireplace?
  1. a fireplace given that the house doesn’t have a second bathroom?
  1. Is having a second bathroom and fireplacedisjoint?
  1. Is having a second bathroom and fireplace independent?
  1. You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities:
  2. The card is a spade, given that it is black
  1. The card is black, given that it is a spade
  1. The card is an ace, given that it is red
  1. The card is a queen, given that it is a face card
  1. You are dealt a hand of three cards, one at a time. Find the probability of each of the following
  2. The first heart you get is the third card dealt
  1. Your cards are all red
  1. You get no spades
  1. You have at least one ace
  1. You get no aces
  1. You get all hearts
  1. The third card is your first red card
  1. You have at least one diamond
  1. The soccer team’s shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described.
  2. The first two you grab are the wrong sizes
  1. The first medium shirt you find is the third one you check.
  1. The first four shirts you pick are all extra-large
  1. At least one of the first four shirts you check is a medium.
  1. The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table

Cholesterol / Blood Pressure
High / OK
High / 0.11 / 0.21
OK / 0.16 / 0.52
  1. What’s the probability that a man has both conditions?
  1. What’s the probability that he has high blood pressure?
  1. What’s the probability that a man with high blood pressure has high cholesterol?
  1. What’s the probability that a man has high blood pressure if it’s known that he has high cholesterol?
  1. Are high blood pressure and high cholesterol mutually exclusive?
  1. Are high blood pressure and high cholesterol independent?
  1. A research went to a local mall and surveyed people from ages 15-25 asking among other things if they had any piercings or tattoos. Below is a two-way table comparing sex to body modification.

Body Modification
Yes / No
Sex / Male / 78 / 67
Female / 115 / 12

If we randomly select a person from this survey:

  1. What is the probability they have a body modification?
  1. What is the probability that we select a female?
  1. What is the probability that we select a female with no body modification?
  1. What is the probability that if we selected a male he has some body modification?
  1. What is the probability that if we selected someone with no body modification that she is a female?
  1. Is Sex and Body Modification mutually exclusive?
  1. Is Sex and Body Modification independent?