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.