Stats Section 4

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

A .400

If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A ∪B) = a. 0.65 b. 0.55 c. 0.10 d. 0.75

A. 0.65 P(A ∪ B) = P(A) + P(B)

If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A | B) = a. 0.05 b. 0.0325 c. 0.65 d. 0.8

A. 05

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called a. permutation b. combination c. multiple step experiment d. None of these alternatives is correct.

A. Permutation

4. If two events are mutually exclusive, then their intersection a. will be equal to zero b. can have any value larger than zero c. must be larger than zero, but less than one d. will be one

A. Will be equal to 0

1. Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is a. 0.25 b. 0.50 c. 1.00 d. 0.75

B. .50

If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is a. 1/6 b. 1/36 c. 1/96 d. 1/216

B. 1/36

Two events with nonzero probabilities a. can be both mutually exclusive and independent b. can not be both mutually exclusive and independent c. are always mutually exclusive d. are always independent

B. Cannot be both mutually exclusive and indpendent

Two events are mutually exclusive a. if their intersection is 1 b. if they have no sample points in common c. if their intersection is 0.5 d. None of these alternatives is correct.

B. If they have no sample points in common

The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A a. must occur b. may occur c. could not occur d. has a 2/3 probability of occurring

B. May Occur

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

B. The intersection of two events

An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is a. 0.500 b. 0.024 c. 0.100 d. 0.900

C. .1 (has to = 1)

If P(A) = 0.48, P(A ∪B) = 0.82, and P(B) = 0.54, then P(A ∩ B) = a. 0.3936 b. 0.3400 c. 0.2000 d. 1.0200

C. .2 (Pu b)= P(a)+P(b)- P(a u b)

If a penny is tossed four times and comes up heads all three times, the probability of heads on the fourth trial is a. zero b. 0.0625 c. 0.5000 d. larger than the probability of tails

C. .5

If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, then P(A ∩ B) = a. 0.00 b. 0.10 c. 0.90 d. 0.20

C. .9

If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪B) = 0.88, then P(B | A) = a. 0.02 b. 0.03 c. 0.04 d. 0.05

C. 04

. From a group of six people, two individuals are to be selected at random. How many possible selections are there? a. 12 b. 36 c. 15 d. 8

C. 15

From nine cards numbered 1 through 9, two cards are drawn. Consider the selection and classification of the cards as odd or even as an experiment. How many sample points are there for this experiment? a. 2 b. 3 c. 4 d. 9

C. 4. 2 draw, odd or even, (2^2)

One of the basic requirements of probability is a. for each experimental outcome Ei, we must have P(Ei) ≥ 1 b. P(A) = P(Ac ) - 1 c. if there are k experimental outcomes, then ∑P(Ei) = 1 d. ∑P(Ei) ≥ 1

C. If there are k experimental outcomes, then sum P(Ei)=1

The addition law is potentially helpful when we are interested in computing the probability of a. independent events b. the intersection of two events c. the union of two events d. conditional events

C. Union of 2 events

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is a. one b. any positive value c. zero d. any value between 0 to 1

C. Zero

If a coin is tossed three times, the likelihood of obtaining three heads in a row is a. zero b. 0.500 c. 0.875 d. 0.125

D. .125

If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A ∪B) = a. 0.07 b. 0.62 c. 0.55 d. 0.48

D. 0.48

Of five letters (A, B, C, D, and E), two letters are to be selected at random (i.e. the order of selection doesn't matter). How many possible selections are there? a. 20 b. 7 c. 5! d. 10

D. 10

. A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is a. 30 b. 100 c. 729 d. 1,000

D. 1000 (10*10*10)

Assume your favorite football 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

D. 9 (outcomes * outcomes, 3*3)

When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the a. relative frequency method b. subjective method c. probability method d. classical method

D. Classical Method

f P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) a. is 0.00 b. is 1.00 c. is 0.5 d. None of these alt. are correct

D. None of these are correct

On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and "cold" weather is .15. Are snow and "cold" weather independent events? a. only if given that it snowed b. no c. yes d. only when they are also mutually exclusive

D. Only when they are also mutually exclusive

35. Bayes' theorem is used to compute a. the prior probabilities b. the union of events c. intersection of events d. the posterior probabilities

D. Posterior probabilities

Initial estimates of the probabilities of events are known as a. sets b. posterior probabilities c. conditional probabilities d. prior probabilities

D. Prior Probabilities

Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment? a. 64 b. 32 Problem Set 4 Page 5 c. 16 d. 4

a. 64 (2^6)

Which of the following statements is always true? a. -1 ≤ P(Ei) ≤ 1 b. P(A) = 1 - P(Ac ) c. P(A) + P(B) = 1 d. ∑P ≥ 1

b P(A)=1-P(Ac)

21. Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.) a. 2 b. 4 c. 12 d. 16

d. 16 (2^4)

The set of all possible outcomes of an experiment is a. an experiment b. an event c. the population d. the sample space

d. The sample space