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A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is
- a)1/20
- b)1/12
- c)3/10
- d)1/2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A box contains 4 red balls and 6 black balls. Three balls are selected...
Solution:
Given, a box contains 4 red balls and 6 black balls.
Total balls = 4 + 6 = 10
Three balls are selected randomly from the box one after another, without replacement.
To find: Probability of selecting one red ball and two black balls.
Let A be the event of selecting one red ball and two black balls.
A can happen in the following ways:
1. RBB
2. BRB
3. BBR
Number of ways of selecting one red ball and two black balls = Number of ways of selecting 1 red ball from 4 red balls x Number of ways of selecting 2 black balls from 6 black balls
= 4C1 x 6C2
= 4 x 15
= 60
Total number of ways of selecting three balls from 10 balls = Number of ways of selecting 3 balls from 10 balls
= 10C3
= (10 x 9 x 8)/(3 x 2 x 1)
= 120
Therefore, the required probability is given by:
P(A) = Number of ways of selecting one red ball and two black balls/Total number of ways of selecting three balls from 10 balls
= 60/120
= 1/2
Hence, the correct option is D.
Given, a box contains 4 red balls and 6 black balls.
Total balls = 4 + 6 = 10
Three balls are selected randomly from the box one after another, without replacement.
To find: Probability of selecting one red ball and two black balls.
Let A be the event of selecting one red ball and two black balls.
A can happen in the following ways:
1. RBB
2. BRB
3. BBR
Number of ways of selecting one red ball and two black balls = Number of ways of selecting 1 red ball from 4 red balls x Number of ways of selecting 2 black balls from 6 black balls
= 4C1 x 6C2
= 4 x 15
= 60
Total number of ways of selecting three balls from 10 balls = Number of ways of selecting 3 balls from 10 balls
= 10C3
= (10 x 9 x 8)/(3 x 2 x 1)
= 120
Therefore, the required probability is given by:
P(A) = Number of ways of selecting one red ball and two black balls/Total number of ways of selecting three balls from 10 balls
= 60/120
= 1/2
Hence, the correct option is D.
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A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box oneafter another, without replacement. The probability that the selected set contains one red ball andtwo black balls isa)1/20b)1/12c)3/10d)1/2Correct answer is option 'D'. Can you explain this answer?
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A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box oneafter another, without replacement. The probability that the selected set contains one red ball andtwo black balls isa)1/20b)1/12c)3/10d)1/2Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box oneafter another, without replacement. The probability that the selected set contains one red ball andtwo black balls isa)1/20b)1/12c)3/10d)1/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box oneafter another, without replacement. The probability that the selected set contains one red ball andtwo black balls isa)1/20b)1/12c)3/10d)1/2Correct answer is option 'D'. Can you explain this answer?.
A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box oneafter another, without replacement. The probability that the selected set contains one red ball andtwo black balls isa)1/20b)1/12c)3/10d)1/2Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box oneafter another, without replacement. The probability that the selected set contains one red ball andtwo black balls isa)1/20b)1/12c)3/10d)1/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box oneafter another, without replacement. The probability that the selected set contains one red ball andtwo black balls isa)1/20b)1/12c)3/10d)1/2Correct answer is option 'D'. Can you explain this answer?.
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