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.