Stats ch4 Online Quiz

A woman has four dress shirts, three pair of slacks and six pair of shoes, assuming these are interchangeable and that shoes can make an outfit, how many different outfits does she have?

4x3x6 = 72

How many four digits numbers are there; that is, using the ten available digits how many integers are there (therefore, can not start with zero) can be formed where repetition allowed.

9x10x10x10 = 9000

A bag contains two blue, three purple, four yellow, two red, three green and one orange marbles. What is the probability that two blue marbles are drawn in succession when chosen with replacement? Give all answers to accurate to at least four demicals; that is, 1/15 = 0.066666666 would be entered as 0.0667. `

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A bag contains two blue, three purple, four yellow, two red, three green and one orange marbles. What is the probability that two green marbles are drawn in succession when chosen without replacement? Give all answers to accurate to at least four decimals; that is, 1/15 = 0.066666666 would be entered as 0.0667.

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A bag contains two blue, three purple, four yellow, two red, three green and one orange marbles.p> What is the conditional probability that, without replacement, the second marble is purple given that the first marble is green? Give all answers to accurate to at least four decimals; that is, 1/15 = 0.066666666 would be entered as 0.0667.

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A group consists of six (6) men and four (4) women; assuming four people are selected at random to form a committee, what is the probability that the committee consist of three (3) men and one (1) woman? Give all answers to accurate to at least four decimals; that is, 1/15 = 0.066666666 would be entered as 0.0667.

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Given E={α, β, γ, δ}, how many combinations are there consisting of three elements selected without replacement.

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Given E={α, β, γ, δ}, how many permutations are there consisting of three elements selected without replacement.

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Given the probability of an event is 0.38, that is P(E)=0.38; the probability that the event will not occur, that is P(E')=?

.62

Given two events, A and B, are mutually exclusive, then P(A|B)=?

0

By definition, what is 0!

1

Given the three events are mutually exclusive and are these simple events form the sample space in union, it the following a probability distribution? P(E1) = 2/3 P(E2) = 1/2 P(E3) = -1/6

False

Given the three events are mutually exclusive and in union these events form the sample space, is the following a probability distribution? P(E1) = 1/3 P(E2) = 1/2 P(E3) = 1/4

False

In an experiment, there are two bags of marbles - in the first bag (X), there are two white (W) and two black (B) marbles and in the second bag (Y), there are three white and one black. An unfair coin is tossed; if a head appears uppermost, then a marble is selected from bag (X); otherwise, a marble is selected from bag (Y). If the probability of a head is 0.6, that is P(X)=0.6. A fair twenty-sided die is used to simulate the above experiment as follows: 1, 2, 3, 4, 5, 6 → XW 7, 8, 9, 10, 11, 12 → XB 13, 14, 15, 16, 17, 18 → YW 19, 20 → YB What justifies using this twenty-sized die to simuluate the above experiment?

Matching probability structures

In a survey of 100 subjects, 63 used brand A, 37 used brand B, and 17 used both brands A and B. What proportion (probability) used either brand A or brand B.

P(A ∪ B) = 63/100 + 37/100 - 17/100 = 83/100 = 0.83 or 83%

In a survey of 100 subjects, 63 used brand A, 37 used brand B, and 17 used both brands A and B. What proportion (probability) used neither brand A nor brand B; that is, not brand A and not brand B.

P(A' ∩ B') = 1 - 83/100 = 0.17 or 17%

If the events A and B are mutually exclusive, then P(A ∪ B)=

P(A) + P(B)

If the events A and B are not mutually exclusive, then P(A ∪ B)=

P(A) + P(B) - P(A ∩ B)

Given two events, A and B, are independent, then P(A∩B)=?

P(A)P(B)

Given two events, A and B, are DEPENDENT, which of the following is true?

P(A|B) = P(A ∩ B)/P(B)

Given two events, A and B, are INDEPENDENT, which of the following is true?

P(A|B) = P(A)

In an experiment, there are two bags of marbles - in the first bag (X), there are two white (W) and two black (B) marbles and in the second bag (Y), there are three white and one black. An unfair coin is tossed; if a head appears uppermost, then a marble is selected from bag (X); otherwise, a marble is selected from bag (Y). If the probability of a head is 0.6, that is P(X)=0.6. What are the associated probabilities in the experiment?

P(XW)=0.3, P(XB)=0.3, P(YW)=0.3 and P(YB)=0.1 P(X)=0.6, P(Y)=0.4, P(W)=5/8 and P(B)=3/8 P(XW)=0.25, P(XB)=0.25, P(YW)=0.375 and P(YB)=0.125

In an experiment, there are two bags of marbles - in the first bag (X), there are two white (W) and two black (B) marbles and in the second bag (Y), there are three white and one black. An unfair coin is tossed; if a head appears uppermost, then a marble is selected from bag (X); otherwise, a marble is selected from bag (Y). That is, select a bag and a marble from that bag. What is the sample space of the experiment? Reminder: the sample space gives outcomes, not (necessarily) frequencies of occurence.

S={XW, XB, YW, YB}

Given the three events are mutually exclusive and in union these events form the sample space, is the following a probability distribution? P(E1) = 0.421 P(E2) = 0.206 P(E3) = 0.373

True

Given the three events are mutually exclusive and in union these events form the sample space, is the following a probability distribution? P(E1) = 1/2 P(E2) = 3/8 P(E3) = 1/8

True

When two cards are drawn from a standard deck of 52 without replacement, the events are ______ and when two cards are drawn from a standard deck of 52 with replacement, the events are ______. Use all lowercase letters. The blank denoted by x and y are either dependent or independent.

dependent, independent

Given two events, A and B, are MUTUALLY EXCLUSIVE, determine which of the following is not true.

n(A ∩ B) = Ø

Given n(E) = 5 and P(E) = 5/12, which of the following is true where P is the probability and O is the odds:

n(S) = 12, n(E') = 7, P(E') = 7/12 and O(E) = 5:7

Given n(E) = a and P(E) = a/b, which of the following is true where P is the probability and O is the odds in terms of a and b:

n(S) = b, n(E') = b - a, P(E') = (b - a)/b and O(E) = a:(b - a)