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?
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 = <<1/6*36=6>>6 cards
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human
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?
gpt
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 = <<1/6*36=6>>6 cards
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