How many events are there? Are the events independent or dependent? If you guess

Question

How many events are there? Are the events independent or dependent? If you guess at each question, what is the probability that you get all of them correct? What is the probability that a person would guess answer A for each question? Assume that you are given a test in which you are to match the correct answers in the right column with the questions in the left column. You can use each answer only once. How many events are there? Are the events independent or dependent? What is the probability of getting them all correct if you are guessing? What is the difference between the two problems?

Explanation / Answer

Solution:

We have 5 question multiple choice quiz. Each with 5 possible answers.

Part 1) How many events are there

Here we define an event as x = number of correct answers

So there could be 0 correct answers, 1 correect answrr, ....., all 5 correct answers

Hence x takes values 0,1,2,3,4,5. Hence there are 6 possible outcomes.

Part 2) Are the events independent or dependent ?

Since each question is different , so answer given to any question does not depends on any other questions. Hence all events are independent.

Part 3) If you guess each question , what is probability that all of them correct?

p = probability of correct answer = 1/ 5

Hence P( all correct answers ) = ( 1 / 5 )^5 = 1 / 3125 = 0.00032

Part 4) what is probability that a person would guess answer A for each question?

So outcome would be like : A A A   A A , this is only one possible outcome which can have answer A for each question and there are total outcomes = 5^5 =3125

Hence P( A for each question ) = 1 / 3125 = 0.00032

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