1. Consider an experiment that consists of rolling a pair of dice. There are 36 possible outcomes for this experiment which are equally likely. What is the probability of getting a total of 3 or 5 for this experiment? (a) 1 /3 (b) 20/36 (c) 1/36 (d) 1/6 (e) 1/2
2. A car dealer sells cars made by different auto manufacturers. Three of these manufacturers are Honda, Nissan, and Ford. Consider an experiment that consists of observing the make and model of the next car sold. The outcomes in the sample space would include simple events such as Nissan Altima and Ford Fusion. Suppose we define the events E1 = Honda, E2=Nissan, and E3=Ford. Note that E1 is not a simple event because there is more than one model of Honda sold (for example, Civic, Accord, and Insight). Based on several years of sales data, the probabilities of these events are estimated as P(E1) 0.25, P(E2) 0.18, and P(E3) 0.14. Based on this data, what is the probability that the next car purchased is not made by one of these three manufacturers? (a) 0.60 (b) 0.57 (c) 0.43 (d) 0.53 (e) 0.32 2
3. A bookstore sells two types of books (fiction and nonfiction) in several formats (hardcover, paperback, digital, and audio). Consider an experiment that consists of observing the type and format of a single book purchase, two possible outcomes are a hardcover fiction book and an audio fiction book. The number of all outcomes the sample space would include is: (a) 4 (b) 16 (c) 32 (d) 8 (e) 12 4.
1. To find the probability of getting a total of 3 or 5 when rolling a pair of dice, we need to count the number of outcomes where the sum of the numbers on the dice is 3 or 5, and divide it by the total number of possible outcomes (36).
The outcomes that give a sum of 3 are (1, 2) and (2, 1), and the outcomes that give a sum of 5 are (1, 4), (2, 3), (3, 2), and (4, 1). So, there are 6 favorable outcomes.
Therefore, the probability of getting a total of 3 or 5 is 6/36, which simplifies to 1/6.
The correct answer is (d) 1/6.
2. The probability that the next car purchased is not made by one of the three manufacturers (Honda, Nissan, and Ford) is equal to 1 minus the sum of the probabilities of the events E1, E2, and E3.
Mathematically, P(not E1 or not E2 or not E3) = 1 - [P(E1) + P(E2) + P(E3)]
Substituting the given probabilities, we get:
P(not E1 or not E2 or not E3) = 1 - (0.25 + 0.18 + 0.14)
= 1 - 0.57
= 0.43
Therefore, the probability that the next car purchased is not made by one of the three manufacturers is 0.43.
The correct answer is (c) 0.43.
3. In this experiment, we are observing the type and format of a single book purchase. There are two possible types (fiction and nonfiction) and four possible formats (hardcover, paperback, digital, and audio).
To find the total number of outcomes in the sample space, we simply multiply the number of possible types by the number of possible formats.
Number of types = 2
Number of formats = 4
Total number of outcomes = Number of types x Number of formats
= 2 x 4
= 8
Therefore, the number of all outcomes in the sample space is 8.
The correct answer is (d) 8.
1. To find the probability of getting a total of 3 or 5 when rolling a pair of dice, we need to determine the number of favorable outcomes and the total number of possible outcomes.
For a total of 3, there is only one combination possible: (1, 2).
For a total of 5, there are four combinations possible: (1, 4), (2, 3), (3, 2), and (4, 1).
Therefore, the total number of favorable outcomes is 1 + 4 = 5.
Since there are 36 equally likely outcomes when rolling a pair of dice, the probability of getting a total of 3 or 5 is 5/36.
The correct answer is (b) 20/36.
2. The probability of an event occurring is given by the formula P(E) = number of favorable outcomes / total number of possible outcomes.
In this case, the event of interest is the next car purchased not being made by one of the three manufacturers (Honda, Nissan, or Ford).
To find the probability, we need to subtract the sum of the individual probabilities of each manufacturer from 1.
P(not Honda, Nissan, or Ford) = 1 - P(Honda) - P(Nissan) - P(Ford)
P(not Honda, Nissan, or Ford) = 1 - 0.25 - 0.18 - 0.14
P(not Honda, Nissan, or Ford) = 0.43
Therefore, the probability that the next car purchased is not made by one of these three manufacturers is 0.43.
The correct answer is (c) 0.43.
3. To determine the number of possible outcomes in the sample space for the purchase of a single book, we need to multiply the number of types (2: fiction and nonfiction) by the number of formats (4: hardcover, paperback, digital, and audio).
Number of possible outcomes = Number of types * Number of formats
Number of possible outcomes = 2 * 4
Number of possible outcomes = 8
Therefore, the number of all outcomes in the sample space would be 8.
The correct answer is (d) 8.