Question

Suppose that on a true/false exam you have no idea at all about the answers to three questions. You choose answersrandomly and therefore have a 50—50 chance of being correct on any one question. Let CCWindicate that you werecorrect on the first two questions and wrong on the third, let WCWindicate that you were wrong on the first and thirdquestions and correct on the second, and so forth.a. List the elements in the sample space whose outcomes are all possible sequences of correct and incorrect responses onyour part.b. Write each of the following events as a set and find its probability:(i) The event that exactly one answer is correct(ii) The event that at least two answers are correct.(ill) The event that no answer is correct.

Answer 1

Answer:

a) Sample spaces (S) whose outcomes are all possible sequences of correct and incorrect responses. The total number for the sample space is 8.

S = {CCC, CCW, CWC, CWW, WCC, WCW, WWC, WWW, }

b)

i) Let E1 = Event that exactly one answer is correct.

Then E1 = {CWW, WCW, WWC}

Prob(E1) = $\frac{3}{8}$

ii) Let E2 = Event that at least two answers are correct

Then E2 = {CCC, CCW, CWC, WCC}

Prob(E2) = $\frac{4}{8}  = \frac{1}{2}$

iii) Let E3 = Event that no answer is correct

Then E3 = {WWW}

Prob(E3) = $\frac{1}{8}$

Step-by-step explanation:

a) First the sample space is listed containing all the possible outcome.

b) i) The event that exactly one answer is correct. First we listed all the combination from the sample space having exactly one correct answer. And they are 3.

Probability = $\frac{number of possible outcome}{number of total outcome}$

Our total outcome is 8.

So, the probability is 3/8.

ii) The event that at least two answers are correct. We listed all the combination having at least two answers from the sample space. And they are 4 in numbers.

So, the probability is 4/8 which is 1/2

iii) The event that no answer is correct. We listed the event with no correct answer from the sample space and we found only 1.

So, the probability is 1/8.