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Answer:
We should expect 25 generated digits in order to get a fifth "4"
Step-by-step explanation:
For each generated digit, there are only two possible outcomes. Either it is a four, or it is not. The probability of a digit being a 4 is independent of other digits. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
The expetcted number of trials to get r sucesses, with p probability, is given by:
Assume that the calculator will generate a "4" on any given attempt with probability 0.20.
This means that
How many total generated digits should we expect in order to get a fifth "4"
This is E when r = 5. So
We should expect 25 generated digits in order to get a fifth "4"