RANDOM PROCESSES AND UNCERTAIN OUTCOMES
Choose the correct answer:
1. When you throw a die (one die, two dice), there are six possible outcomes
that have an equal chance of happening. In other words, if you throw the
die fairly, your chance of getting number 1 or 2 or 3 or 4 or 5 or 6 is
exactly the same.
2. When you re-throw the die:
a. The chances of throwing the same number as before are less (e.g. if
you've thrown a 4 before, the chances of getting a 4 again are smaller).
b. The chances of throwing the same number as before are greater (e.g.
if you've thrown a 4 before, the chances are greater that you'll throw
a 4 again).
c. It makes no difference to the outcome - each outcome is as likely to
come up again as it has at any time in the past and as at any time in
3. When Herschelle Gibbs, the cricketer, bats in a cricket match we can
correctly predict his score if we know how fit he is, the state of the opposition
team, the condition of the pitch, and his batting average in previous games.
a. True - because these factors determine the outcome.
b. False - because even though these factors may affect the outcome, we
can never be sure because there are too many complex factors and
too much uncertainty.
4. When Herschelle Gibbs comes out to bat a second time in the same cricket
match, his chances of getting the same score as before remain identical.
a. True - because we can correctly predict his score, based on how he
performed in the first innings. That is, we can now see how well he is
feeling that day, we now know the state of the opposition team and
now know the condition of the pitch. That is, we know all the factors
that may affect the outcome.
b. False - because when Gibbs comes out to bat for a second time, lots
of things have changed, making it impossible to know beforehand
what his score in the second innings will be.
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5. If you know nothing about the six horses running in a particular
horse race, the outcome is uncertain and your chances of picking the
winning horse are 1 in 6.
a. True - since you don't know anything about the factors that may affect
the outcome (e.g. the condition of the horse, the jockey's previous
performance, etc) your chance of picking the winner are
1 in 6.
b. False - the outcome of the race is certain beforehand, even if you don't
know what it will be.
6. If you are told that 4 of the horses running in the race are lame, then the
result is still uncertain, but you have a better chance of picking the winner
(i.e. one of the 2 fit horses):
a. True - You now know that 4 horses out of the 6 will definitely not win
and you can place your bet on one of the 2 non-lame horses,
increasing your chances of winning to 1 in 2.
b. False - there are six horses running and so the chances of any one of
the six winning remain the same.
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