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A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is?
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**Solution:**
To find the probability that the last ball drawn is white, we need to consider two possible scenarios:
1. The white balls are drawn before the red balls.
2. The red balls are drawn before the white balls.
Let's calculate the probabilities for each scenario:
**Scenario 1: White balls are drawn before red balls**
In this scenario, we need to calculate the probability of drawing all the white balls before the red balls.
The probability of drawing the first white ball is 2/5 since there are two white balls out of a total of five balls.
After drawing the first white ball, there will be four remaining balls in the bag, with one white ball and three red balls.
The probability of drawing the second white ball is 1/4 since there is one white ball out of the four remaining balls.
Finally, after drawing the second white ball, there will be three remaining balls in the bag, all of which are red.
Therefore, the probability of drawing all the white balls before the red balls in Scenario 1 is:
P(White before Red) = (2/5) * (1/4) = 2/20 = 1/10
**Scenario 2: Red balls are drawn before white balls**
In this scenario, we need to calculate the probability of drawing all the red balls before the white balls.
The probability of drawing the first red ball is 3/5 since there are three red balls out of a total of five balls.
After drawing the first red ball, there will be four remaining balls in the bag, with two white balls and two red balls.
The probability of drawing the second red ball is 2/4 since there are two red balls out of the four remaining balls.
Finally, after drawing the second red ball, there will be two remaining balls in the bag, both of which are white.
Therefore, the probability of drawing all the red balls before the white balls in Scenario 2 is:
P(Red before White) = (3/5) * (2/4) = 6/20 = 3/10
**Probability that the last ball drawn is white**
To find the probability that the last ball drawn is white, we need to consider both scenarios.
The probability of the last ball being white is equal to the probability of drawing all the white balls before the red balls in Scenario 1 plus the probability of drawing all the red balls before the white balls in Scenario 2.
Therefore, the probability that the last ball drawn is white is:
P(Last Ball White) = P(White before Red) + P(Red before White) = 1/10 + 3/10 = 4/10 = 2/5
Therefore, the probability that the last ball drawn is white is 2/5 or 0.4.
To find the probability that the last ball drawn is white, we need to consider two possible scenarios:
1. The white balls are drawn before the red balls.
2. The red balls are drawn before the white balls.
Let's calculate the probabilities for each scenario:
**Scenario 1: White balls are drawn before red balls**
In this scenario, we need to calculate the probability of drawing all the white balls before the red balls.
The probability of drawing the first white ball is 2/5 since there are two white balls out of a total of five balls.
After drawing the first white ball, there will be four remaining balls in the bag, with one white ball and three red balls.
The probability of drawing the second white ball is 1/4 since there is one white ball out of the four remaining balls.
Finally, after drawing the second white ball, there will be three remaining balls in the bag, all of which are red.
Therefore, the probability of drawing all the white balls before the red balls in Scenario 1 is:
P(White before Red) = (2/5) * (1/4) = 2/20 = 1/10
**Scenario 2: Red balls are drawn before white balls**
In this scenario, we need to calculate the probability of drawing all the red balls before the white balls.
The probability of drawing the first red ball is 3/5 since there are three red balls out of a total of five balls.
After drawing the first red ball, there will be four remaining balls in the bag, with two white balls and two red balls.
The probability of drawing the second red ball is 2/4 since there are two red balls out of the four remaining balls.
Finally, after drawing the second red ball, there will be two remaining balls in the bag, both of which are white.
Therefore, the probability of drawing all the red balls before the white balls in Scenario 2 is:
P(Red before White) = (3/5) * (2/4) = 6/20 = 3/10
**Probability that the last ball drawn is white**
To find the probability that the last ball drawn is white, we need to consider both scenarios.
The probability of the last ball being white is equal to the probability of drawing all the white balls before the red balls in Scenario 1 plus the probability of drawing all the red balls before the white balls in Scenario 2.
Therefore, the probability that the last ball drawn is white is:
P(Last Ball White) = P(White before Red) + P(Red before White) = 1/10 + 3/10 = 4/10 = 2/5
Therefore, the probability that the last ball drawn is white is 2/5 or 0.4.
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A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is?
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A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is?.
A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 5 balls, three red and two white. Balls are randomly removed one at a time without replacement until all the red balls are drawn or all the white balls are drawn. The probability that the last ball drawn is white, is?.
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