Marcus takes a deck of standard playing cards and takes out all the face cards and the 8's. Mark picks a card at random and then replaces it 36 times. How many times should he expect to pick a card that's both red and has a number divisible by 3?
Thoughts? Step-by-step reasoning:
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Without the face cards and the 8's, there are 9 cards of each suit. Half these cards are red, and 3 / 9 have numbers divisible by 3, so the odds of drawing a card divisible by 3 are 1 / 3. Multiply the odds of drawing a red card by the odds of drawing a card divisible by 3 to find the odds of both things happening: 1 / 3 * 1 / 2 = 1 / 6. Finally, multiplying the probability of drawing a red / 3 - divisible card by the number of cards Mark draws to find how many he should expect to meet his criteria: 1 / 6 * 36 cards = 6 cards.
Thus, the answer is 6.
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