Let a 52 deck of numbered cards be created as follows:
2 special cards: 0 and 1
25 powers of 2: 2, 4, 8, ..., 2^25
25 powers of 3: 3, 9, 27, ..., 3^25
Shuffle the deck and draw at random 3 cards. Evaluate the product of the 3 numbers, say P.
What is the probability of P=0?
What is the probability of P being a non zero integer square?
What is the probability of P being a 4-digit number?
(In reply to
Part 1 and 2 solutions by Brian Smith)
This agrees with my computer total.
Initially I was worrying that the test for being a square was being overwhelmed by numbers larger than could be handled by the square root function losing the extended precision, but then I substituted smaller odd and even powers in the deck, WLOG:
'0 1 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3 4 9 2 3'
and still came out with 6200 cases.
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Posted by Charlie
on 2023-03-29 10:52:26 |
re: Part 1 and 2 solutions
