2. Suppose that you are given five shapes, each containing a number, as shown below: 1 2 3 (i) You choose exactly one shape at random. Assuming that the probability of choosing each shape is equal, what is the expected number of sides of the shape that you select? (ii) We repeat the experiment in part (i), but now suppose that each number describes the probability that you choose that shape (out of 10). For example, the triangle with a 4 will be chosen with a probability of 4/10, while the square 2 will be chosen with a probability 2/10. What is the expected number of sides?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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2. Suppose that you are given five shapes, each containing a number, as shown below:
1
4
2
3
(i) You choose exactly one shape at random. Assuming that the probability of choosing each shape is
equal, what is the expected number of sides of the shape that you select?
(ii) We repeat the experiment in part (i), but now suppose that each number describes the probability
that you choose that shape (out of 10). For example, the triangle with a 4 will be chosen with a
probability of 4/10, while the square 2 will be chosen with a probability 2/10. What is the expected
number of sides?
Transcribed Image Text:2. Suppose that you are given five shapes, each containing a number, as shown below: 1 4 2 3 (i) You choose exactly one shape at random. Assuming that the probability of choosing each shape is equal, what is the expected number of sides of the shape that you select? (ii) We repeat the experiment in part (i), but now suppose that each number describes the probability that you choose that shape (out of 10). For example, the triangle with a 4 will be chosen with a probability of 4/10, while the square 2 will be chosen with a probability 2/10. What is the expected number of sides?
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