1Consider all possible ways you could select two numbers fro

1.Consider all possible ways you could select two numbers from a pool of numbers that only equally likely contains 2, 3, 5, and 6.

That is, if define a random variable X for the possible number, X has the following probability model:

X

2

3

5

6

Pr(X)

0.25

0.25

0.25

0.25

a). What is the probability model (sample space and probability) of the two numbers in your hand?

b). What is the probability model of the number of odd numbers in your hand?

c).What is the probability model of the proportion of odd numbers in your hand?

d). What is the probability model of the average of the two numbers in your hand?

Solution

the probability model (sample space and probability) of the two numbers in your hand

There are 16 possibilities with equal probability

Hence the sample space is (2,2)... (2,6) (3,2)......(6,6)

Prob for each outcome = 0.0625.

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Prob for odd number =

Except (2,2)(2,6) (6,2) and (6,6) all others have odd numbers

Hence prob = 0.0625(12) = 0.75

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proportion of odd numbers is possible except if both are odd.

So it contains all except (3,3) (3,5),,,,

There are 4 like that

prob = 12(0.0625) = 0.75

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Average of two numbers =