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To find the probability of rolling a three on the red dye and a four on the blue dye, we need to first calculate the individual probabilities of rolling each number.
The probability of rolling a three on the red dye is 1/5 because there is only one three on a five-sided die.
The probability of rolling a four on the blue dye is 1/10 because there is only one four on a ten-sided die.
To find the probability of both events happening, we multiply the individual probabilities:
(1/5) * (1/10) = 1/50
So, the probability of rolling a three on the red dye and a four on the blue dye is 1/50.