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.
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