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?
Yes, you are correct in finding the probability that the first 0 occurs as the fifth random digit generated.
To calculate this probability, you multiply the probabilities of not getting a zero for the first four times (9/10 each time) by the probability of getting a zero on the fifth trial (1/10).
So the probability is:
(9/10) × (9/10) × (9/10) × (9/10) × (1/10) = (9^4) / (10^5)
To find how many digits you would expect to have to generate in order to observe the first zero, we can calculate the expected value.
The expected value represents the average number of times you would have to repeat the experiment (in this case, generating random digits) in order to observe the event of interest (in this case, generating a zero).
In each trial, the probability of generating a zero is 1/10. So, on average, you would have to repeat the experiment 1 / (1/10) = 10 times to observe a zero.
Therefore, you would expect to have to generate 10 digits in order to observe the first zero.