assignment 01

GEM2900, 2013/2014 Semester II Assignment 01

InstructionsThis is the first of a series of assignments for this module.Each correct answer to a question is worth two (2) marks.

This question sheet is available from the module workbin folder.Please make sure that you submit your answers via the IVLE assessment facility.

Submission period: Wednesday 5 Feb, 12pm to Wednesday 12 Feb, 12pm.

A maximum of two attempts will be allowed for this assessment. However, if you have madetwo attempts, only the last attempt to this assessment will be graded.

Exercise 1.You and your friend, Ah Heng, visit the race course. You two are interested in betting on ahorse, named HorSey, involved in the race. The bookie offers odds of 4 to 1 against for HorSey.Ah Heng suggests that instead of betting with the bookie, you’ll simply bet with each otherwith the odds published by the bookie (4 to 1 against for HorSey). Ah Heng also gives youthe option of either placing the bets with him or receiving the bets from him. You do a quickassessment on HorSey and think the horse’s chance of winning the race is about 33%. Wouldyou prefer to place or receive the bets if you must play the game with your friend, Ah Heng?

Choose one of the following options.

(a) Receive the bets from Ah Heng.

(b) Place the bets with Ah Heng.

(c) It doesn’t really matter.

Exercise 2.Suppose that you have agreed to settle a dispute with your friend, Ahmad, by tossing a coin.The problem is that neither one of you has any coin. You happen to have a bottle drink withyou, so Ahmad suggests that you use the bottle cap, which will count as heads if it lands withtop up, and tails otherwise. How would you play the game to guarantee the fairness in settlingthe dispute?

Figure 1: Left: heads (top up); right: tails

National University of Singapore



(a) Toss the bottle cap once. Ahmad wins if the cap lands on ‘tails’; you win, otherwise.

(b) Toss the bottle cap twice. Ahmad wins if the two tosses landed with the same side up.That is, Ahmad wins if the bottle cap landed HH or TT.

(c) Toss the bottle cap twice. Ahmad wins if the bottle cap landed with the sequence HT; youwin if the bottle cap landed with the sequence TH. If nobody wins, you start all over againuntil someone wins.

(d) As you are not sure if the bottle cap will land with P (H) = P (T ) = 1/2, you can’tguarantee the fairness.

Exercise 3.Which is the most likely sequence to turn up if a fair coin is being tossed 4 times?

(a) HHHH

(b) HTHH

(c) HTHT

(d) TTTH

(e) All equally likely.

Exercise 4.With a random toss of a fair coin what is your estimate of the probability of a Head afterTTTTTTT?

(a) 0

(b) Between 0 and 0.5

(c) 0.5

(d) Between 0.5 and 1

(e) 1

Exercise 5.Go over to YouTube and watch the video “How stats fool juries” by Peter Donnelly:http://www.youtube.com/watch?v=hoD2TjjypyM

Donnelly’s coin toss experiment demonstrates which of the following?

(a) On average, it takes more coin tosses to see the HTH pattern than it does to see HTT.

(b) The HTT pattern, on average, requires more coin tosses than HTH.

(c) The average number of tosses to get HTT is the same as the number to get HTH.

(d) There are people out there with a lot of coins and a lot of time.

(e) Hold up! Nobody told me there would be word problems!


http://www.youtube.com/watch?v=hoD2TjjypyM


Exercise 6.Consider an experiment where a biased 5-sided die with faces painted with the numbers 1,2,3,4and 5 is rolled once. For this die, the probabilities of obtaining the numbers 1,2,3,4 and 5 aregiven as

P ({1}) = 2/16, P ({2}) = P ({3}) = P ({4}) = 3/16, P ({5}) = 5/16.

Let A = {1, 2, 3}, B = {1, 2, 4}, and C = {1, 3, 4}.

Consider the following statements:

(I) The three events are pairwise independent.

(II) The three events are mutually independent.

(III) Events A and B are independent; Events A and C are not independent; Events B andC are not independent.

(IV) Events A and B are not independent; Events A and C are independent; Events B andC are independent.


(a) Only statement (I) is correct.

(b) Only statement (II) is correct.

(c) Both statements (I) & (II) are correct.

(d) Only statement (III) is correct.

(e) Only statement (IV) is correct.

(f) None of the statements is correct.

Exercise 7.Suppose P (A) = 0.4, P (B) = 0.3, and P (AB) = 0. Which one of the following statementscorrectly defines the relationship between events A and B?

(a) A and B are independent, but not mutually exclusive.

(b) A and B are mutually exclusive, but not independent.

(c) A and B are neither mutually exclusive nor independent.

(d) A and B are both mutually exclusive and independent.


assignment 01

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