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An urn contains 10 yellow balls and 10 blue balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a yellow ball in the second draw is(round up to 1 decimal place)
Correct answer is '0.5'. Can you explain this answer?
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An urn contains 10 yellow balls and 10 blue balls. In the first draw,...
Introduction
In this problem, we have an urn containing 10 yellow balls and 10 blue balls. We are asked to find the probability of drawing a yellow ball in the second draw, given that one ball has already been picked and discarded without noticing its color.
Solution
To solve this problem, we need to consider the total number of balls remaining in the urn and the number of yellow balls remaining.
Step 1: Calculate the total number of balls remaining
Since one ball has already been picked and discarded, there are now 19 balls remaining in the urn (10 yellow balls + 10 blue balls - 1 discarded ball).
Step 2: Calculate the number of yellow balls remaining
Since we do not know the color of the ball that was discarded, there are two possible scenarios:
1. If the discarded ball was yellow, there are now 9 yellow balls remaining in the urn.
2. If the discarded ball was blue, there are still 10 yellow balls remaining in the urn.
Step 3: Calculate the probability of drawing a yellow ball in the second draw
To calculate the probability, we need to divide the number of favorable outcomes (drawing a yellow ball) by the total number of possible outcomes (drawing any ball).
In the first scenario (discarded ball was yellow), the probability of drawing a yellow ball in the second draw is 9/19 ≈ 0.474 (rounded to one decimal place).
In the second scenario (discarded ball was blue), the probability of drawing a yellow ball in the second draw is 10/19 ≈ 0.526 (rounded to one decimal place).
Since we do not know which scenario occurred, we need to consider both possibilities and calculate the average probability.
Average probability = (0.474 + 0.526) / 2 = 0.5
Therefore, the probability of drawing a yellow ball in the second draw is approximately 0.5.
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An urn contains 10 yellow balls and 10 blue balls. In the first draw,...
P(yellow) = (10x9 + 10x10)/20x19 = ½ = 0.5
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An urn contains 10 yellow balls and 10 blue balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a yellow ball in the second draw is(round up to 1 decimal place)Correct answer is '0.5'. Can you explain this answer?
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