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    Q: A calculator claims it can randomly generate a digit from 0-9. For any 4 digits generated, the probabibility of 2 zeros is 0.03. Is the calculators claim correct?

    A: No, if it was, the probability of 2 zeros would be 0.0486

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    There are 10 digits altogether.

    The prob of a 0 is 1/10, the prob of not getting = is 9/10

    You need two zeros and two non-zeros, usual rules apply about multiplying the probabilities together. ------(1)

    However, for 4 digits, there are actually 6 ways the zeros can appear. They could be eg the first two digits drawn, or they could be the first and third, or they could be the last two etc. In total, there are 6 ways (try it and see)

    So your prob (1) above needs to be multipled by 6.
 
 
 
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Updated: February 20, 2018
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