Question

1) A candidate sits for an examination consisting of 20 MCQ questions. All questions consist of 4 options, each option equally as likely to be the correct answer. 2 marks are awarded if a question is answered correctly, 1 mark is deducted if incorrectly answered, and no marks are awarded if a question was left blank.
The candidate realises he has a 50% probability of correctly answering each of the questions Q1 to Q10, but he does not know how to answer Q11 to Q20 and has to resort to random selection. Which of the following strategies should he adopt to maximize his expected total mark?

A) Leave the entire paper blank

B) Answer only Q1 to Q10, leave Q11 to Q20 blank

C) Answer all questions

D) Answer only Q11 to Q20, leave Q1 to Q10 blank

2) A bag contains 20 chocolate balls of two flavours (milk and dark), and two wrapper colours (blue and red). There are 8 dark chocolates and 7 milk chocolates that have a blue wrapper, and there are 2 dark chocolates and 3 milk chocolates that have red wrapper. A student randomly selects a chocolate from the bag. Assume the chocolates are indistinguishable from one another during selection. Which of the following statements is true?

A) P(milk) < P(milk|red wrapper)

B) P(milk) = P(milk|red wrapper)

C) P(milk) > P(milk|red wrapper)

3) Let A and B be two distinct events in a sample space with P(A) ≠ 0 and P(B) ≠ 0. Which of the following statements is/are definitely true?

(I) If A and B are independent, then P(A|B) = P(B|A).

(II) If A and B are mutually exclusive, then P(A|B) = P(B|A).

A) Only II is true.

B) Only I is true.

C) Neither statements are true.

D) Both I and II are true.

4) A fortune teller specialising in predicting the outcome of coin flips claims that he can successfully predict the outcome of a coin flip 60% of the time. You suspect that he is actually more accurate than what he claims to be and decide to do a hypothesis test. What should the null and alternative hypothesis be?

A) H0 : P(success) = 0.5, H1 : P(success) > 0.6

B) H0 : P(success) = 0.5, H1 : P(success) > 0.5

C) H0 : P(success) = 0.5, H1 : P(success) < 0.6

D) H0 : P(success) = 0.6, H1 : P(success) < 0.6

E) H0 : P(success) = 0.6, H1 : P(success) > 0.6

5) A student flips a coin 100 times and lands heads 35% of the time. You want to show that this has not happened due to chance and that the coin is indeed biased against landing heads. To test such a hypothesis, what should the null and alternative hypotheses be?

A) H0 : P(heads) = 0.5, H1 : P(heads) < 0.5

B) H0 : P(heads) = 0.35, H1 : P(heads) < 0.35

C) H0 : P(heads) = 0.5, H1 : P(heads) > 0.5

D) H0 : P(heads) = 0.35, H1 : P(heads) > 0.35

*PLEASE ANSWER ALL THE ABOVE QUESTIONS & TYPE YOUR ANSWER (NO SCREENSHOTS OR IMAGES) IN OPTION (A), (B), (C), (D) & (E), WITH SHORT EXPLANATION. THANK YOU IN ADVANCE

Answer 1

1) C, because 1 to 10 questions will give him atleaat 50% and he should try remaining because not all his answers are going to be wrong.

2) C, because probability of getting milk chocolates is greater as there are 10 milk chocolates in all so it's probability becomes greater than milk chocolates with red wrapper as there are only 3 milk chocolates with red wrapper.

3) A, because if A and B are mutually exclusive then there will be no common element in them,thus there intersection probability will be zero. Hence P(A|B) and P(B|A) will be zero , i.e equal.

4)E, because since fortune teller claims he is 60% successful,P(success)=0.6 and as we see he is more accurate than 60% the probability becomes greater than 60%.

5) B, because student says he gets 35% head P(head)=0.35 and ee know coin is biased then it should be less than 35% so P(head)<0.35