A probability problem by Alex Alex
One deck of cards consists of six cards numbered 1 through 6, and a second deck consists of six cards numbered 7 through 12. If one card is chosen at random from each deck, and the numbers on these cards are multiplied, what is the probability that this product is an even number? Give your answer to two decimal places.
The answer is 0.75.
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1 solution
We can solve this by taking the converse of another probability. The only two possible outcomes are that the product is even or it is odd. 1 - P(even) = P(odd). The only way to get an odd product is to have both numbers odd. The probability of an odd number in the first deck is 2 1 , and it is the same in the second as well. These probabilities multiply to 4 1 . So 1 - 4 1 = 4 3 , which is 0 . 7 5 in decimal form.