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A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ?
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A bag contain 6 blue, 4 red, and 5 green balls. If three balls are dra...
Problem: A bag contains 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement, find the probability of getting utmost one color.
Solution:
Step 1: Total number of ways to draw three balls without replacement
Total number of ways to draw three balls without replacement = Total number of ways to choose 3 balls out of 15 balls = 15C3 = (15*14*13)/(3*2*1) = 455
Step 2: Probability of getting all balls of the same color
Probability of getting all balls of the same color = (6C3 + 4C3 + 5C3)/455 = (20+4+10)/455 = 34/455 = 0.0747
Step 3: Probability of getting two balls of one color and one ball of another color
Probability of getting two balls of one color and one ball of another color = (6C2*4C1 + 6C1*4C2 + 6C1*5C2)/455 = (90+72+60)/455 = 222/455 = 0.4879
Step 4: Probability of getting one ball of each color
Probability of getting one ball of each color = (6C1*4C1*5C1)/455 = 120/455 = 0.2637
Step 5: Probability of getting utmost one color
Probability of getting utmost one color = Probability of getting all balls of the same color + Probability of getting two balls of one color and one ball of another color + Probability of getting one ball of each color = 0.0747 + 0.4879 + 0.2637 = 0.8263
Therefore, the probability of getting utmost one color when three balls are drawn randomly without replacement is 0.8263.
Solution:
Step 1: Total number of ways to draw three balls without replacement
Total number of ways to draw three balls without replacement = Total number of ways to choose 3 balls out of 15 balls = 15C3 = (15*14*13)/(3*2*1) = 455
Step 2: Probability of getting all balls of the same color
Probability of getting all balls of the same color = (6C3 + 4C3 + 5C3)/455 = (20+4+10)/455 = 34/455 = 0.0747
Step 3: Probability of getting two balls of one color and one ball of another color
Probability of getting two balls of one color and one ball of another color = (6C2*4C1 + 6C1*4C2 + 6C1*5C2)/455 = (90+72+60)/455 = 222/455 = 0.4879
Step 4: Probability of getting one ball of each color
Probability of getting one ball of each color = (6C1*4C1*5C1)/455 = 120/455 = 0.2637
Step 5: Probability of getting utmost one color
Probability of getting utmost one color = Probability of getting all balls of the same color + Probability of getting two balls of one color and one ball of another color + Probability of getting one ball of each color = 0.0747 + 0.4879 + 0.2637 = 0.8263
Therefore, the probability of getting utmost one color when three balls are drawn randomly without replacement is 0.8263.
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A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ?
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A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ?.
A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contain 6 blue, 4 red, and 5 green balls. If three balls are drawn randomly without replacement then find the probability of getting utmost one colour ?.
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