Two decks of cards are there. Each deck contains 20 cards, with numbers from 1 to 20 written on them. A card is drawn of random from each deck, getting the numbers x and y what is the probability that log x + log y is a positive integer. Logs are taken to the base 10.
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Answer:
7/400
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Two decks of cards are there. Each deck contains 20 cards, with numbers from 1 to 20 written on them. A card is drawn of random from each deck, getting the numbers x and y what is the probability that log x + log y is a positive integer. Logs are taken to the base 10
log(x + y) = logxy
log 10 = 1 & Log100 = 2 ( 0 is not a +ve integer)
only positive integer possible are 1 & 2
When xy = 10 & xy = 100
xy = 10 ( 1* 10 , 2*5 , 5 * 2 , 10 *1)
xy = 100 (5 * 20 , 10* 10 , 20 * 5)
Total 7 cases out of 20 * 20 = 400
Probability = 7/400
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