Probability Explanation And Exercises Worksheet Page 37
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37so in case of a 4-choice question, your guess chance is 0.25). Your instructor
offers you the opportunity to choose amongst the following exam formats: I. 6
questions of the 4-choice type; you pass when 5 or more answers are correct;
II. 5 questions of the 5-choice type; you pass when 4 or more answers are
correct; III. 4 questions of the 10-choice type; you pass when 3 or more
answers are correct. Rank the three exam formats according to their
attractiveness. It should be clear that the format with the highest probability to
pass is the most attractive format. Which would you choose and why?
26. Consider the question of whether the home team wins more than half of its
games in the National Basketball Association. Suppose that you study a simple
random sample of 80 professional basketball games and find that 52 of them
are won by the home team.
a. Assuming that there is no home court advantage and that the home team
therefore wins 50% of its games in the long run, determine the probability that
the home team would win 65% or more of its games in a simple random
sample of 80 games.
b. Does the sample information (that 52 of a random sample of 80 games are
won by the home team) provide strong evidence that the home team wins more
than half of its games in the long run? Explain.
27. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11
plums, and 2 mangos.
a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit
at random. What is the probability that you will pull out a pear?
b. Imagine now that you put your hand in the refrigerator and pull out a piece
of fruit. You decide you do not want to eat that fruit so you put it back into the
refrigerator and pull out another piece of fruit. What is the probability that the
first piece of fruit you pull out is a banana and the second piece you pull out is
an apple?
c. What is the probability that you stick your hand in the refrigerator one time
and pull out a mango or an orange?
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