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stats please help test tom

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When a computerized generator is used to generate random digits, the proability that any particular digit in the set {0,1,2, . . .,9} is generated on any individual trial is 1/10-0.1. suppose that we are generating digits one at a time and are interested in tracking occurrences of the digit 0.

Determine the probabiliy that the first 0 occurs as the fifth random digit generated?

so the probability of not getting a zero for the first four time is 9/10. then the probability of getting a zero for the fifth time is 1/10. and i just multiply that right.

how many digits would you expect to have to generate in order to observe the first o.

please help me. am i doing this right?

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