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Chapter 5: Problem 64

If a person is given the choice of an integer from 0 to 9 , is it more likely that he or she will choose an integer near the middle of the sequence than one at either end? a. If the integers are equally likely to be chosen, find the probability distribution for \(x\), the number chosen. b. What is the probability that a person will choose a \(4,5,\) or \(6 ?\) c. What is the probability that a person will not choose a \(4,5,\) or \(6 ?\)

Short Answer

Expert verified
Answer: The probability of choosing 4, 5, or 6 is 3/10, and the probability of not choosing 4, 5, or 6 is 7/10.

Step by step solution

01

Define the sample space and event

The sample space S is the set of all possible outcomes when a person chooses a number from 0 to 9. In this case, the sample space is S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
02

Find the probability distribution for x

Since the person is equally likely to choose any integer from 0 to 9, the probability of choosing any number is 1/10 (since there are 10 possible choices). So, the probability distribution for x is: P(x) = 1/10 for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
03

Find the probability of choosing 4, 5, or 6

We are asked to find the probability that a person chooses 4, 5, or 6. Since the events are mutually exclusive (a person can only choose one number), we can simply add the probabilities of each event: P(4, 5, or 6) = P(4) + P(5) + P(6) = (1/10) + (1/10) + (1/10) = 3/10.
04

Find the probability of not choosing 4, 5, or 6

We are asked to find the probability of not choosing a 4, 5, or 6. We can find this probability by subtracting the probability of choosing 4, 5, or 6 from 1: P(not 4, 5, or 6) = 1 - P(4, 5, or 6) = 1 - 3/10 = 7/10. So, the probability that a person will not choose a 4, 5, or 6 is 7/10.

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