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There are 13 yellow cards, 6 blue, 10 red, and 8 green cards in a stack of cards faced down. Once a card is selected, it is not replaced. Find the probability of 2 blue cards

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Final answer:

The probability of drawing two blue cards without replacement from a stack of 37 cards is found by multiplying the probability of drawing a blue card on the first draw (6/37) by the probability of drawing a blue card on the second draw (5/36), after the first blue card has been removed.

Step-by-step explanation:

The student is asking about the probability of drawing two blue cards from a stack without replacement. To find this probability, we use the formula for conditional probability. The total number of cards is 37 (13 yellow + 6 blue + 10 red + 8 green).

The probability of drawing one blue card is 6/37. Once a blue card is drawn, there are 5 blue cards left, and the total number of cards is reduced to 36. Therefore, the probability of drawing a second blue card is 5/36.

Finally, the probability of drawing two blue cards in succession without replacement is the product of the two individual probabilities:

  • P(1st blue card) = 6/37
  • P(2nd blue card | 1st blue card) = 5/36
  • Total probability = (6/37) * (5/36)

Use a calculator to multiply these fractions together to get the final probability.

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