Three balls are drawn successively from the box containing 6 white balls 5 red balls and 4 blue ball find the probability that they are drawn in the order blue red and white if each ball is replaced or not replaced
replaced: 4/15 * 5/15 * 6/15
not replaced: 4/15 * 5/14 * 6/13
To find the probability of drawing the balls in the specific order blue, red, and white, we need to consider two scenarios: with replacement and without replacement.
1. With replacement:
When a ball is drawn with replacement, it is placed back into the box before drawing the next ball. This means that the probabilities of drawing each ball remain the same for each draw.
The probability of drawing a blue ball is 4/15 (4 blue balls out of a total of 15 balls).
The probability of drawing a red ball is also 5/15 (5 red balls out of 15 balls).
The probability of drawing a white ball is 6/15 (6 white balls out of 15 balls).
Since the draws are independent with replacement, the probability of drawing them in the specific order blue, red, and white is given by multiplying the individual probabilities:
P(with replacement) = (4/15) * (5/15) * (6/15) = 1/15.
2. Without replacement:
When a ball is drawn without replacement, it is not placed back into the box before drawing the next ball. This means that the probabilities of drawing each ball change for each subsequent draw.
The probability of drawing a blue ball on the first draw is 4/15 (4 blue balls out of a total of 15 balls).
The probability of drawing a red ball on the second draw is 5/14 (5 red balls out of the remaining 14 balls).
The probability of drawing a white ball on the third draw is 6/13 (6 white balls out of the remaining 13 balls).
Since the draws are dependent without replacement, the probability of drawing them in the specific order blue, red, and white is given by multiplying the individual probabilities:
P(without replacement) = (4/15) * (5/14) * (6/13) ≈ 0.0433 (rounded to four decimal places).
Therefore, the probability of drawing the balls in the order blue, red, and white is 1/15 with replacement, and approximately 0.0433 without replacement.
To find the probability of drawing the balls in the order blue-red-white, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Let's start with the scenario where the balls are replaced after each draw:
Total Number of Outcomes:
In the first draw, there are a total of 6 + 5 + 4 = 15 balls to choose from.
In the second draw, after replacement, there are still 15 balls to choose from.
In the third draw, after replacement, there are still 15 balls to choose from.
Therefore, the total number of outcomes is 15 * 15 * 15 = 3375.
Number of Favorable Outcomes:
To draw in the order blue-red-white, we need to select a blue ball first, then a red ball, and finally a white ball.
Number of ways to select a blue ball = 4 (since there are 4 blue balls).
Number of ways to select a red ball = 5 (since there are 5 red balls).
Number of ways to select a white ball = 6 (since there are 6 white balls).
Therefore, the number of favorable outcomes is 4 * 5 * 6 = 120.
Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
= 120 / 3375
≈ 0.0356 (rounded to 4 decimal places)
Now let's consider the scenario where the balls are not replaced after each draw:
Total Number of Outcomes:
In the first draw, there are a total of 6 + 5 + 4 = 15 balls to choose from.
In the second draw, after not replacing, there are 14 balls to choose from (since one ball has already been drawn).
In the third draw, after not replacing, there are 13 balls to choose from (since two balls have already been drawn).
Therefore, the total number of outcomes is 15 * 14 * 13 = 2730.
Number of Favorable Outcomes:
To draw in the order blue-red-white, we need to select a blue ball first, then a red ball, and finally a white ball.
Number of ways to select a blue ball = 4 (since there are 4 blue balls).
Number of ways to select a red ball = 5 (since there are 5 red balls).
Number of ways to select a white ball = 6 (since there are 6 white balls).
Therefore, the number of favorable outcomes is 4 * 5 * 6 = 120.
Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
= 120 / 2730
≈ 0.0440 (rounded to 4 decimal places)
Thus, the probability of drawing the balls in the order blue-red-white is approximately 0.0356 when the balls are replaced after each draw, and approximately 0.0440 when the balls are not replaced after each draw.