1. Cousider a random number generator designed for equally likely outcomes. That

Question

1. Cousider a random number generator designed for equally likely outcomes. That is, each random digit between 0 and 9, inclusive has an equal probability of being selected. (a) State the sample space for the random digits. (b) Let an event A be observing a 5. What would you expect the probability of observing igits were generated what proportion of digits would you expect to be 5)? Can you generalize this to each possible random digit/outcome in the sample space? (c) What is A? ) Each outcome in a sample space must have probability between 0 and 1, and the total of the probabilities must equal 1. Show that your assignment of probabilities in part b satisfies this rule.

Explanation / Answer

a)

Sample space = {0,1,2,3,4,5,6,7,8,9}

b)

From law of large numbers, probablity of getting 5 = 1/10 = 0.1

Yes, we can generalize to each outcome fo the sample space

c)

A is event of observing 5.

Ac will be event of not observing 5 i.e. {0,1,2,3,4,6,7,8,9}

d)

It satisfies the rule pf probability

Digit Probability 0 0.1 1 0.1 2 0.1 3 0.1 4 0.1 5 0.1 6 0.1 7 0.1 8 0.1 9 0.1 Total 1

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