Learn how to build an E-Commerce site with Angular 5, a JavaScript framework used by developers to build web, desktop, and mobile applications.

Hi,

I know the answer to this question but I am not sure how they worked it out. I know the method to work it out.

'

Steve, Katerina and Jess are three students who have agreed to take part in a psychology experiment. Each student is to answer several sets of multiple-choice questions. Each set has the same number of questions, n, where n is a number greater than 20. For each question there are four possible options (A, B, C or D), of which only one is correct.

If Katerina answers a question correctly, the probability that she will answer the next question correctly is 3/4 . If she answers a question incorrectly, the probability that she will answer the next question incorrectly is 2/3

.

In a particular set, Katerina answers Question 1 incorrectly.

b. i. Calculate the probability that Katerina will answer Questions 3, 4 and 5 correctly.

ii. Find the probability that Katerina will answer Question 25 correctly. Give your answer correct to

four decimal places.

I know the answer to this question but I am not sure how they worked it out. I know the method to work it out.

'

Steve, Katerina and Jess are three students who have agreed to take part in a psychology experiment. Each student is to answer several sets of multiple-choice questions. Each set has the same number of questions, n, where n is a number greater than 20. For each question there are four possible options (A, B, C or D), of which only one is correct.

If Katerina answers a question correctly, the probability that she will answer the next question correctly is 3/4 . If she answers a question incorrectly, the probability that she will answer the next question incorrectly is 2/3

.

In a particular set, Katerina answers Question 1 incorrectly.

b. i. Calculate the probability that Katerina will answer Questions 3, 4 and 5 correctly.

ii. Find the probability that Katerina will answer Question 25 correctly. Give your answer correct to

four decimal places.

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with Premium.
Start your 7-day free trial.

I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

then the probability of answering question n+1 correctly is

p*(3/4) + (1-p)*(1-2/3) = (4+5*p)/12

the probability of answering question n+2 correctly would then be

(4+5*((4+5*p)/12))/12

etc.

after 25 questions the probability will be getting very close to satisfying

P = (4+5*P)/12

Then what is your question?

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial
Math / Science

From novice to tech pro — start learning today.

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with Premium.
Start your 7-day free trial.

1. Question 2 is answered correctly. The chance for that is 2/3. The chance to answer q3 correctly are now 3/4 (because q2 was correctly answered), then the chance for q4 is again 3/4 and for q5 it's again 3/4. This makes 2/3 x 3/4 x 3/4 x 3/4 = 0.28125

2. Question 2 is answered incorrectly. The chance for that is 1/3. The chance to answer q3 correctly are now 2/3 (because q2 was incorrectly answered), then the chances for q4 and q5 remain 3/4 (because the previous question was answered correctly). This makes 1/3 x 2/3 x 3/4 x 3/4 = 0.125

Now we sum both probabilities to get the total probability: 0.40625