How to find most likely number?

Probability that an apple picked at random from a sack is bad is 0.15.

What’s the most likely number of bad apples in a sample of 30 apples?

The answer is 4

2 Answers

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  • rotchm
    Lv 7
    3 months ago
    Favorite Answer

    If you have N apples to choose from, there are then on average 0.15 * N bad ones.

    With N=30 this gives 4.5 bad apples. 

    Since you can only have integer # of apples, then you must look at the closest possibilities (because we assume that the distribution is bell shaped). So lets look at 

    m = 4 and m = 5.

    To have exactly m bad ones, we use:

    https://en.wikipedia.org/wiki/Binomial_distributio...

    That is,

    Prob_exactly _m_bad = 30Cm * 0.15^m * (1-0.15)^(30-m).

    If m = 4 what do you get?

    If m = 5 what do you get?

    Which is higher (meaning, more likely).

    that's your answer.

    Done!

     

  • 3 months ago

    P(bad) = 0.15

    From a batch of 30 we would have 30(0.15) => 4.5

    so, 4 or 5 apples

    :)>

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