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发帖数: 199 | 1 there is a box of 100 cards, with 10 cards for each of numbers, 0, 1, 2,...,
9. Draw 3 cards without replacement. What is the distributon of the sum of
3 cards? i.e., is there a general formula? | y***s
发帖数: 23 | 2 Use conditional probability. Just some thoughts.
A:={among the 3 cards, 3 cards are the same}
B:={among the 3 cards, 2 cards are the same}
C:={all the three cards are distinct }
Then we can compute P(A), P(B), and P(C).
Let S is an event, e.g. S={the sum of the three cards = 5}
P(S)=P(S|A)P(A) + P(S|B)P(B) + P(S|C)P(C).
We need to find the conditional prob. of
P(S|A), P(S|B), and P(S|C).
For P(S|A),
P(S=3*1|A)=10/100*9/100*8/100, the same for
0,2,...9.
For P(S|C),
P(S=3|C)=P(S=4|C)=P(S=5|C)=....P(S=7+8+9)=10/100*90/100*80/100.
For P(S|B),
Left to the reader. I'm lazy. |
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