To determine the probability of drawing a red ball and then a blue ball from a bag with replacement, we first need to know the total number of balls and how many of them are red and blue. However, let's illustrate the general process for calculating the probability.
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Scenario Setup: Assume you have a bag that contains a certain number of red and blue balls. Let's denote:
- \( R \) = number of red balls
- \( B \) = number of blue balls
- \( T \) = total number of balls = \( R + B \)
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Probabilities Calculation:
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Probability of drawing a red ball (first draw): This probability is given by the ratio of the number of red balls to the total number of balls: \[ P(\text{red}) = \frac{R}{T} \]
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Probability of drawing a blue ball (second draw): Since the draw is with replacement, the total number of balls remains unchanged when you draw the blue ball. Thus, the probability of drawing a blue ball is: \[ P(\text{blue}) = \frac{B}{T} \]
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Combined Probability: The two events (drawing a red ball and then drawing a blue ball) are independent because of the replacement. Therefore, the probability of both events occurring in sequence is found by multiplying the probabilities: \[ P(\text{red then blue}) = P(\text{red}) \times P(\text{blue}) = \left(\frac{R}{T}\right) \times \left(\frac{B}{T}\right) \] \[ P(\text{red then blue}) = \frac{R \times B}{T^2} \]
In conclusion, you will need the numbers of red and blue balls in order to compute the specific probability. But using the formula provided, you can calculate it once you have those values.