Question

onsider a random number generator designed for equally likely outcomes. If numbers between 0 and 99 are​ chosen, determine which of the following is not correct. a. If 100 numbers are generated comma each integer between 0 and 99 must occur exactly once. b. For each random number generated comma each integer between 0 and 99 has probability 0.01 of being selected. c. If a very large number of random numbers are generated comma then each integer between 0 and 99 would occur close to 1 % of the time. d. The cumulative proportion of times that a 0 is generated tends to get closer to 0.01 as the number of random numbers generated gets larger and larger.

Answer 1

The following option is not correct:

(a) If 100 numbers are generated comma each integer between 0 and 99 must occur exactly once.

Explanation:

This is not correct, as there is a possibility of an integer being generated twice when 100 numbers are generated.

This can be explained with an example such as stated below:

3 numbers are to be generated.

The number generated can either be 1, 2, or 3.

The probability for all three numbers to be generated once when the generator is run 3 times is:

(1/3)*(1/3)*(1/3) * Number of ways to arrange the three numbers

Thus this probability will be:

Probability = (1/3)^3 * 3!

Probability = 0.222

Since the probability here is not equal to 1, the probability for the same thing happening at a larger scale will also not be 1.