A Professor of Finance has noted from past experience that students who
do all their assignments have a 90% chance of passing the final exam, and
if they don’t do any of the assignments they have a 15% chance of passing
the final exam. The Professor estimates that 65% of students have done
their assignments. Based on these information,
(a) What percentage of students passed the final exam? (5%)
(b) Given that a student passed the final exam, what is the probability they
completed their assignments? (5%)
An advertisement claims that two out of five doctors recommend a certain
toothpaste. A random sample of 20 doctors is selected, and it is found that
only two of them recommend the product.
(a) Assuming the advertising claim is true, what is the probability of the
observed event? (5%)
(b) Given the sampling results, do you believe the advertisement? Explain.(5%)
There are 3 boxes. The first box contains 2 white balls and 2 black balls;
the second box contains 2 white balls and 1 black ball; while the third box
contains 1 white ball and 3 black balls.
(a) From each box, a ball is randomly drawn. Compute the probability that
all 3 balls drawn are white. (5%)
(b) One box is randomly selected, then a ball is randomly drawn from this
box. Compute the probability that the ball drawn is white. (5%)
Based on this information, and assume that the history of stocks A and B
is a useful guide to what may be expected of them in the future.
(a) If you were to invest in the stock with the highest average return, which
stock would you choose and why? (5%)
(b) If you were to invest in the stock with the least risk, which stock would
you choose and why? (5%)
(a) Define random variables. (5%)
(b) Should “tossing a fair dice” be considered a random variable? Why or
why not? (5%)
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