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A cent or more? (Posted on 2017-05-01) Difficulty: 2 of 5
Mary had exactly 21 coins in her purse, total value of a round dollar.
While counting her money, she dropped a coin.

Evaluate the probability it was a penny.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts conditional nature of the problem (spoilers) | Comment 1 of 2
The distribution of coins in Mary's purse could be any of the following, showing columns for halves, quarters, dimes, nickels and pennies:

    h q d n  p
    0 0 3 13 5
    0 0 7 4 10
    0 1 3 7 10
    0 2 3 1 15
    1 0 2 3 15
If these distributions were equally likely the overall probability would be the average of the individual probabilities, 55/105 = 11/21 or approximately .523809523809524.

But half-dollars are rare; the fifth set of coins listed is highly unlikely. Also people tend to put their pennies in jars, either at home or in a "leave a penny take a penny" jar near a cash register, so the low penny counts would tend to have a higher probability of being the initial situation. On the other hand I can't imagine wanting 13 nickels in one's purse either. Situations 2 and 3 would seem the likeliest, in either of which case the probability asked for (that is, conditionally now) would be 10/21.

  Posted by Charlie on 2017-05-01 08:56:54
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