Probability of Two Independent Extractions
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50. In a bag are 3 red balls and 7 green balls, indistinguishable by touch. Two extractions are made, with the first ball being returned to the bag before the second extraction. What is the probability of extracting 2 green balls? A) $\frac{51}{100}$ B) $\frac{42}{90}$ C) $\frac{7}{10}$ D) $\frac{49}{100}$ E) $\frac{9}{100}$
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Hi Ersan, let's solve this probability problem together. We need to find the probability of extracting two green balls from a bag with replacement.
Probability with Replacement
First, let's list the contents of the bag. We have three red balls and seven green balls.
- Red balls: 3
- Green balls: 7
The total number of balls in the bag is the sum of red and green balls, which is ten.
The probability of drawing a green ball in a single draw is the number of green balls divided by the total number of balls.
The problem states that the first ball is returned to the bag before the second extraction. This means the events are independent, and the probabilities remain the same for both draws.
Independent Events: Since the ball is replaced, the probability remains $ rac{7}{10}$ for each draw.
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