GEM2900, 2014/2015 Semester I Assignment 01

Answers

1. The possible answers are (a) & (b)

We can adopt the

relative frequency interpretation of probability. Spin the pointer a large number oftimes and count the proportion of times the pointer falls in the grey region. Thatwill serve as the probability that the spinner stops on the grey region.

propensity/classical interpretation of probability. The probability of the spinner stop-ping on the grey region can be computed as the angle of the grey sector divided by360 degrees.

2. The answer is (e).

The tosses are independent and have no memory.

3. The answer is (c).

We are talking about a fair coin here!

4. The answer is (a).

We are asked forP (CC|CC CC CC),

where CC denotes that the first card is not a club, the second card is. etc.

Note that

P (CC CC CC) = 13/52 12/51 + 13/52 39/51 + 39/52 13/51.

Thus the required probability is

P (CC|CC CC CC) =13/52 12/51

13/52 12/51 + 13/52 39/51 + 39/52 13/51= 2/15 0.133.

5. Note: All the statements are always false except for (IV), which is possibly true.

6. The answer is (a). Watch the video again.

7. The possible answers are (b) & (c)

Define event A = {HorSey wins the race}. The implied probability based on the oddsoffered (3 to 1 against) is P (A) = 25%. However, you personal belief for P (A) is 33%,which is translated to odds of 2 to 1 against. You would place the bets with someonewhen the odds based on your personal belief are lower than the odds offered. So youwould place the bets with Heng Heng if you think the probability of winning is greaterthan 25% and receive bets from Heng Heng when it is lower.

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