a. Use the multiplication rule to find P(WWC), where C denotes a correct answer

Question

a. Use the multiplication rule to find P(WWC), where C denotes a correct answer and W denotes a wrong answer.

P(WWC)equals=

(Type an exact answer.)

b. Beginning with WWC, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list.

P(WWC)minussee above

P(WCW)equals=

P(CWW)equals=

(Type exact answers.)

c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?

(Type an exact answer.)

Explanation / Answer

The details are not there that how many choices we have out of which one should be correct. Suppose there are k choices (For example, in a true - false question, there are two choices so k = 2). Then,

P(Correct) = P(C) = 1/k

P(Wrong) = P(W) = 1 - P(C) = 1 - 1/k

So,

a) P(WWC)

= P(W)*P(W)*P(C)

= (1 - 1/k) * (1 - 1/k) * (1/k)

= (k - 1)2 / k3

b) P(WCW)

= P(W) * P(C) * P(W)

= (1 - 1/k) * (1/k) * (1 - 1/k)

= (k - 1)2 / k3

P(CWW)

= P(C) * P(W) * P(W)

= (1/k) * (1 - 1/k) * (1 - 1/k)

= (k - 1)2 / k3

c) P(Exactly one correct)

= P(CWW) + P(WCW) + P(WWC)

= 3(k - 1)2 / k3

The exact answers can be found by putting the value of k according to the questions. [k = Number of choices we have]

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