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Exam 5: Probability

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Question 51

Multiple Choice

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How many ways can we choose three items at random without replacement from five items (A, B, C, D, E) if the order of the selected items is not important?

A) 60
B) 120
C) 10
D) 24

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Question 52

Multiple Choice

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Given the contingency table shown here, find P(E) . $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Major }$ $\begin{array} {| c | c | c | c | c| } \hline\text { Gender } & \text { Accounting } ( A ) & \text { Gen. Mgmt. } ( G ) & \text { Economics } ( E ) & \text { Row Total } \\\hline\text { Male } ( M ) & 210 & 180 & 140 & 530 \\\hline \text { Female } ( F ) & 150 & 160 & 160 & 470 \\\hline \quad \text { Col Total } & 360 & 340 & 300 & 1000\\\hline\end{array}$

A) .180
B) .300
C) .529
D) .641

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Question 53

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Given the contingency table shown here, if a survey participant is selected at random, what is the probability he/she is an undergrad who favors the change to a quarter system? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Group Surveyed }$ $\begin{array}{|c|c|c|c|c|}\hline \text { Opinion: } &\text { Undergrads }(U) & \text { Graduates }(G) & \text { Faculty }(F) & \text { Row Total } \\\hline \text { Oppose Change (N) } &73 & 27 & 20&120 \\\hline \text { Favor Change (S) } &27 & 23 & 30&80 \\\hline \text { Col Total } &100 & 50 & 50&200 \\\hline\end{array}$

P(A | B) is the joint probability of events A and B divided by the probability ofA.

If events A and B are mutually exclusive, the joint probability of the events is zero.

The union of two events is all outcomes in either or both, while the intersection is only those events in both.

If events A and B are mutually exclusive, then P(A) + P(B) = 0.

The sum of the probabilities of all compound events in a sample space equals one.

When two events A and B are independent, the probability of their intersection can be found by multiplying their probabilities.

Debbie has two stocks, X and Y. Consider the following events: X = the event that the price of stock X has increased Y = the event that the price of stock Y has increased The event "the price of stock X has increased and the price of stock Y has not increased" may be written as

Given the contingency table shown here, what is the probability that a student attends a public school in a rural area? $\text { What type of school do you attend? }$ $\begin{array}{|c|c|c|c|c|}\hline \text { Location } &\text { Public }(P) & \text { Religious }(R) & \text { Other Private }(O) & \text { Row Total } \\\hline \text { Inner City (I) }&35 & 15 & 20&70 \\\hline \text { Sububan (S) }&45 & 10 & 25&80 \\\hline \text { Rural (R) }&25 & 5 & 5&35 \\\hline \text { Col Total }& 105 & 30 & 50&185 \\\hline\end{array}$

A sample space is the set of all possible outcomes in an experiment.

P(A∩B) = .50 is an example of a joint probability.

The following probabilities are given about events A and B in a sample space: P(A) = 0.30, P(B) = 0.40, P(A or B) = 0.60. We can say that:

The general law of addition for probabilities says P(A or B) = P(A) + P(B) - P(A∩B).

If P(A) = 0.35, P(B) = 0.60, and P(A or B) = 0.70, then:

Given the contingency table shown here, if a faculty member is chosen at random, what is the probability he/she opposes the change to a quarter system? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Group Surveyed }$ $\begin{array}{|c|c|c|c|c|}\hline \text { Opinion: } &\text { Undergrads }(U) & \text { Graduates }(G) & \text { Faculty }(F) & \text { Row Total } \\\hline \text { Oppose Change (N) } &73 & 27 & 20&120 \\\hline \text { Favor Change (S) } &27 & 23 & 30&80 \\\hline \text { Col Total } &100 & 50 & 50&200 \\\hline\end{array}$

Given the contingency table shown here, find P(R?L) . Survey question: Do you plan on retiring or keep working when you turn 65? $\begin{array} { | l | c | c | c | } \hline\text { Employee } & \text { Retire } ( R ) & \text { Work } ( W ) & \text { Total }\\\hline \text { Management } ( M ) & 13 & 18 &31 \\\hline \text { Line worker } ( L ) & 39 & 54 & 93 \\\hline \text { Total } & 52 & 72 & 124\\\hline\end{array}$

Given the contingency table shown here, find P(L or W) . Survey question: Do you plan on retiring or keep working when you turn 65? $\begin{array} { | l | c | c | c | } \hline\text { Employee } & \text { Retire } ( R ) & \text { Work } ( W ) & \text { Total }\\\hline \text { Management } ( M ) & 13 & 18 &31 \\\hline \text { Line worker } ( L ) & 39 & 54 & 93 \\\hline \text { Total } & 52 & 72 & 124\\\hline\end{array}$

The odds of an event can be calculated by dividing the event's probability by the probability of its complement.