Math  /  Data & Statistics

QuestionMultiple-choice questions each have four possible answers ( a,b,c,da, b, c, d ), one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find P(WCC)\mathrm{P}(\mathrm{WCC}), where C denotes a correct answer and W denotes a wrong answer. P(WCC)=364P(W C C)=\frac{3}{64} (Type an exact answer.) b. Beginning with WCC, make a complete list of the different possible arrangements of two correct answers and one wrong answer, then find the probability for each entry in the list. P(WCC) see above P(CCW)=P(CWC)=\begin{array}{l} \mathrm{P}(\mathrm{WCC})-\text { see above } \\ \mathrm{P}(\mathrm{CCW})=\square \\ \mathrm{P}(\mathrm{CWC})=\square \end{array} (Type exact answers.)

Studdy Solution
For CWC:
P(CWC)=P(C)×P(W)×P(C)=(14)×(34)×(14)P(CWC) = P(C) \times P(W) \times P(C) = \left(\frac{1}{4}\right) \times \left(\frac{3}{4}\right) \times \left(\frac{1}{4}\right)
P(CWC)=364P(CWC) = \frac{3}{64}
The probabilities are:
P(WCC)=364P(CCW)=364P(CWC)=364\begin{array}{l} \mathrm{P}(\mathrm{WCC}) = \frac{3}{64} \\ \mathrm{P}(\mathrm{CCW}) = \frac{3}{64} \\ \mathrm{P}(\mathrm{CWC}) = \frac{3}{64} \end{array}

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