3.1 Introduction to Probability
Identify the sample space for the following situation.
rolling a six sided die
What is
{1, 2, 3, 4, 5, 6} ?
Determine whether the events are independent or dependent. Explain your reasoning.
A ball is selected from a bin of balls numbered from 1 through 52. It is replaced, and then a second numbered ball is selected from the bin.
What is independent? Since the first ball is replaced, the probability for the second draw is not changed.
Determine whether the events are mutually exclusive. Explain.
Event A: Randomly select a student with a birthday in April.
Event B: Randomly select a student with a birthday in May.
What is, yes, they are mutually exclusive? A student cannot have a birthday in April and in May.
A 12-sided die with sides numbered 1 through 12 is rolled. Assuming that all sides are equally likely to be rolled, what is the probability that the number rolled is a multiple of 3?
What is 0.333 or 33.3%?
If two cards are drawn without replacement from a standard deck, find the probability that the second card is black, given that the first card is a spade.
What is 0.490 or 49.0%?
There are four blood types: O, A, B, and AB. For each person, they are either Rh-positive (+) or Rh-negative (-). Identify the sample space and the number of possible outcomes.
What is {O+, O-, A+, A-, B+, B-, AB+, AB-} and 8 possible outcomes?
The probability that an African American person in the United States has type O+ blood is 47%. Six unrelated African American people in the United States are selected at random. Find the probability that none of the six have type O+ blood.
What is 0.0222?
A card is selected at random from a standard deck of cards. Find the probability of randomly selecting a club or a 3.
What is 0.308 or 30.8%?
Someone thinks of a 2-digit number (the first digit cannot be 0) and asks you to guess what it is. What is the probability that your first guess will be correct?
What is 0.0111 or 1.11%?
Suppose that 39% of a town’s population have type O blood, 15% are Rh-negative, and 7% have type O blood and are Rh-negative. What is the probability that a randomly selected individual in the town will have either type O blood or be Rh-negative?
What is 0.47 or 47%?
You are purchasing a new car. The possible manufacturers you can by from are Ford, GM, and Honda. The possible car sizes to choose from are compact and midsize. The colors you have to choose from are white, red, black, and green. How many different ways can you select one manufacturer, one car size, and one color?
What is 24 different ways?
In a recent year, about 1.6% of all infants born in the U.S. were conceived through in vitro fertilization (IVF). Of the IVF deliveries, about 41.5% resulted in multiple births. Find the probability that a randomly selected infant was conceived through IVF and was part of a multiple birth.
What is 0.00664 or 0.664%?
You roll a die. Find the probability of rolling a 5 or a number greater than 3.
What is 0.5 or 50%?
Two marbles are drawn without replacement from a jar with four black and three white marbles. Find the probability that the first marble is black and the second is white.
What is 0.286 or 28.6%?
If five cards are drawn without replacement from a standard deck, find the probability that all five cards are diamonds.
What is 0.000495 or 0.0495%?
How many license plates can you make when a license plate consists of six (out of 26) alphabetical letters, each of which can be repeated but the first letter cannot be A, B, C, or D?
What is 261,390,272 different license plates?
In a recent year, about 1.6% of all infants born in the U.S. were conceived through in vitro fertilization (IVF). Of the IVF deliveries, about 41.5% resulted in multiple births. Find the probability that a randomly selected infant was conceived through IVF and was not part of a multiple birth.
What is 0.00936 or 0.936%?
Of the cans produced by a company, 96% do not have a puncture, 93% do not have a smashed edge, and 89.3% do not have a puncture and do not have a smashed edge. Find the probability that a randomly selected can does not have a puncture or a smashed edge.
What is 0.997 or 99.7%?
If two cards are drawn without replacement from a standard deck, find the probability that the second card is a heart, given that the first card is a heart.
What is 0.0588 or 5.88%?
A box of 15 chocolates has 6 that are caramel, 5 that contain coconut, and 4 that are strawberry filled. If you randomly select 3 chocolates, what is the probability that you will get all coconut filled?
What is 0.00220 or .220%?
Given: P(A)=0.08. Find P(A').
What is P(A')=0.92?
According to a study, 80% of K-12 schools or districts in the United States use digital content such as ebooks, audio books, and digital textbooks. Of these 80%, 4 out of 10 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as a part of their curriculum.
What is 0.32 or 32%?
A couple plans to have four children. Assuming that boys and girls are equally likely, find the probability that the couple will have at least one boy.
What is 0.938 or 93.8%?
A card is drawn from a standard deck of cards. What are the odds that a king or queen is drawn?
What is 2:11?
A pet shop has 10 puppies, 6 of them males. There are 3 beagles (1 male) 1 cocker spaniel (male), and 6 poodles. Construct a two-way table and find the probability that one of these puppies, chosen at random, is a beagle, given that it is a male.
What is 0.167 or 16.7%?