Question 1

Of five letters (A, B, C, D, and E), two letters are to be selected at random.How many possible are possible?
A) 20
B) 7
C) 5!
D) 10

Accepted Answer

The number of ways to choose 2 letters out of 5 is calculated using combinations: C(5,2) = 5! / (2!(5-2)!) = 10.

Question 2

The symbol ∩ shows the
A) union of events.
B) intersection of two events.
C) sum of the probabilities of events.
D) sample space.

Accepted Answer

The symbol ∩ represents the intersection of two events, meaning the overlap or common elements between the two events. Option A refers to the symbol ∪, which represents the union of events, meaning the combination or total elements of the two events. Option C is not related to the symbol ∩ or any other probability notation. Option D refers to the set of all possible outcomes in a probability experiment, denoted by the symbol Ω or S.

Question 3

Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female.The number of sample points in this experiment is
A) 2.
B) 4.
C) 6.
D) 8.

Accepted Answer

The answer of Three applications for admission to a local...

Question 4

If a coin is tossed three times, the likelihood of obtaining three heads in a row is
A) 0.0.
B) 0.500.
C) 0.875.
D) 0.125.

Accepted Answer

The probability of getting one head in a single toss is 0.5. The probability of getting three heads in a row is the product of the individual probabilities, so it is 0.5 × 0.5 × 0.5 = 0.125. Therefore, the answer is D.

Question 5

Each customer entering a department store will either buy or not buy some merchandise.An experiment consists of following 3 customers and determining whether or not they purchase any merchandise.The number of sample points in this experiment is
A) 2.
B) 4.
C) 6.
D) 8.

Accepted Answer

The answer of Each customer entering a department store will...

Question 6

An experiment consists of three steps.There are four possible results on the first step, three possible results on the second step, and two possible results on the third step.The total number of experimental outcomes is
A) 9.
B) 14.
C) 24.
D) 36.

Accepted Answer

The total number of experimental outcomes is found by multiplying the number of outcomes in each step. Thus, the total number of outcomes is 4 x 3 x 2 = 24. Therefore, the correct choice is (C).

Question 7

The union of events A and B is the event containing all the sample points belonging to
A) B or A.
B) A or B.
C) A or B or both.
D) A or B, but not both.

Accepted Answer

The union of two events A and B includes all the sample points that are in A, in B, or in both A and B.

Question 8

Assume your favorite soccer team has 2 games left to finish the season.The outcome of each game can be win, lose or tie.The number of possible outcomes is
A) 2.
B) 4.
C) 6.
D) 9.

Accepted Answer

For each game, there are 3 possible outcomes (win, lose, or tie). Since there are 2 games, we must multiply the number of outcomes for each game to find the total number of possible outcomes. Thus, 3 x 3 = 9, so there are 9 possible outcomes. Therefore, the best choice is D.

Question 9

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =
A) 0.400.
B) 0.169.
C) 0.390.
D) 0.650.

Accepted Answer

Since A and B are independent events, P(A ∩ B) = P(A) * P(B). Given P(A ∩ B) = 0.26 and P(A) = 0.65, we can solve for P(B) as follows: P(B) = P(A ∩ B) / P(A) = 0.26 / 0.65 = 0.4.

Question 10

The multiplication law is potentially helpful when we are interested in computing the probability of
A) mutually exclusive events.
B) the intersection of two events.
C) the union of two events.
D) conditional events.

Accepted Answer

The multiplication law states that the probability of the intersection of two events is equal to the product of their individual probabilities if the events are independent. Therefore, the multiplication law is most helpful when we are interested in computing the probability of the intersection of two events.

Question 11

If two events are independent, then
A) they must be mutually exclusive.
B) the sum of their probabilities must be equal to one.
C) their intersection must be zero.
D) the product of their probabilities gives their intersection.

Accepted Answer

Independence means that the occurrence of one event does not affect the probability of the other event occurring. Therefore, the probability of their intersection (both events occurring) is simply the product of their individual probabilities.

Question 12

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is
A) 0.
B) 1/16.
C) 1/2.
D) larger than the probability of tails.

Accepted Answer

The probability of getting heads on any one toss of a fair coin is 1/2. However, each coin toss is independent of the previous tosses. So, the fact that the penny came up heads three times in a row does not affect the probability of it coming up heads on the fourth toss. Therefore, the probability of getting heads on the fourth trial is still 1/2, which is choice C.

Question 13

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is
A) much larger than any other outcome.
B) much smaller than any other outcome.
C) 1/6.
D) 1/216.

Accepted Answer

The outcome of the third trial is independent of the outcomes of the first two trials. Therefore, the probability of rolling a "3" on the third trial remains the same as any other trial, which is 1/6. The previous outcomes do not affect the probability of the next outcome.

Question 14

The sum of the probabilities of two complementary events is
A) 0.
B) 0.5.
C) 0.57.
D) 1.0.

Accepted Answer

The sum of the probabilities of two complementary events is 1. This is because if one event is the complement of the other event, then they together make up the entire sample space. Therefore, the probability of one event plus the probability of its complement must be equal to 1.

Question 15

An experiment consists of tossing 4 coins successively.The number of sample points in this experiment is
A) 16.
B) 8.
C) 4.
D) 2.

Accepted Answer

Since each coin can have 2 outcomes (heads or tails), the total number of sample points is found by multiplying the number of outcomes for each coin. Therefore, the total number of sample points for tossing 4 coins successively is 2x2x2x2 = 16.

Question 16

Bayes' theorem is used to compute
A) the prior probabilities.
B) the union of events.
C) intersection of events.
D) the posterior probabilities.

Accepted Answer

Bayes' theorem is used to compute the posterior probabilities, which are updated probabilities of an event after new information has been taken into account. It allows us to update our beliefs based on new evidence or data.

Question 17

The symbol ∪ shows the
A) union of events.
B) intersection of two events.
C) sum of the probabilities of events.
D) sample space.

Accepted Answer

The symbol ∪ represents the union of events, which is the event that either one or the other event occurs (or both).

Question 18

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =
A) 0.14.
B) 0.43.
C) 0.75.
D) 0.59.

Accepted Answer

P(B) can be found using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Given P(A ∪ B) = 0.69, P(A) = 0.4, and P(A ∩ B) = P(A)P(B | A) = 0.4 * 0.35 = 0.14, we can solve for P(B) = 0.69 - 0.4 + 0.14 = 0.43.

Question 19

The set of all possible outcomes of an experiment is
A) a sample point.
B) an event.
C) the population.
D) the sample space.

Accepted Answer

The set of all possible outcomes of an experiment is called the sample space. It contains all the possible outcomes, or sample points, that could occur in the experiment. Therefore, the correct answer is D, sample space.

Question 20

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?
A) 1/52
B) 2/52
C) 3/52
D) 4/52

Accepted Answer

The answer of Assuming that each of the 52 cards...

Quiz 4: Introduction to Probability

Of five letters (A, B, C, D, and E) , two letters are to be selected at random.How many possible are possible?

The symbol ∩ shows the

Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female.The number of sample points in this experiment is

If a coin is tossed three times, the likelihood of obtaining three heads in a row is

Each customer entering a department store will either buy or not buy some merchandise.An experiment consists of following 3 customers and determining whether or not they purchase any merchandise.The number of sample points in this experiment is

An experiment consists of three steps.There are four possible results on the first step, three possible results on the second step, and two possible results on the third step.The total number of experimental outcomes is

The union of events A and B is the event containing all the sample points belonging to

Assume your favorite soccer team has 2 games left to finish the season.The outcome of each game can be win, lose or tie.The number of possible outcomes is

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

The multiplication law is potentially helpful when we are interested in computing the probability of

If two events are independent, then

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

The sum of the probabilities of two complementary events is

An experiment consists of tossing 4 coins successively.The number of sample points in this experiment is

Bayes' theorem is used to compute

The symbol ∪ shows the

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

The set of all possible outcomes of an experiment is

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?