Multiplication rule to find P(CWC) Are they correct? Thank you Multiple-choice q

Question

Multiplication rule to find P(CWC)

Are they correct? Thank you

Multiple-choice questions each have four possible answers (a, 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(CWC), where C denotes a correct answer and W denotes a wrong answer P(CWC)= (Type an exact answer.) b. Beginning with CWC, 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(CWC)-see above P(WCC) = 164 PCCW) = 164 | Type exact answers.) c. Based on the preceding results, what is the probability of getting exactly two correct answers when three guesses are made? Type an exact answer.) 32

Explanation / Answer

Here, P(C)=P(Correct answer)=1/4

& P(W)=P(Wrong answer)=3/4

(a) We have to find here P(CWC)

Consider,

P(CWC)=P(C)*P(W)*P(C)=(1/4)*(3/4)*(1/4)=3/64 ......Using multiplication rule

(b) We have to find here P(WCC).

Consider.

P(WCC)=P(W)*P(C)*P(C)=(3/4)*(1/4)*(1/4)=3/64   ......Using multiplication rule

We have to find here P(CCW).

Consider.

P(CCW)=P(C)*P(C)*P(W)=(1/4)*(1/4)*(3/4)=3/64   ......Using multiplication rule

(c) We have to find here the probability of getting exactly getting two answers correctly when three guesses are made..

P(getting exactly getting two answers correctly)=P(CWC)+P(WCC)+P(CCW)=3/64+3/64+3/64=9/64

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