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Four red balls, four green balls and four blue balls are put in a box. Three balls are pulledout of the box at random one after another without replacement. The probability thatall the three balls are red is
- a)1/72
- b)1/55
- c)1/36
- d)1/27
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Four red balls, four green balls and four blue balls are put in a box....
Probability that all the three balls are red is
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The required probability can also be obtained as,
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The required probability can also be obtained as,
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Most Upvoted Answer
Four red balls, four green balls and four blue balls are put in a box....
Problem:
Four red balls, four green balls, and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all three balls are red is:
Solution:
To find the probability that all three balls pulled out are red, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When three balls are pulled out one after another without replacement, the total number of outcomes can be calculated using the concept of permutations. Since there are twelve balls in total, the first ball can be any of the twelve, the second ball can be any of the remaining eleven, and the third ball can be any of the remaining ten. Therefore, the total number of outcomes is:
Total outcomes = 12 * 11 * 10 = 1320
Number of favorable outcomes:
Since we want all three balls to be red, we need to choose three red balls out of the four available. The number of ways to choose three red balls out of four is given by the combination formula:
Number of favorable outcomes = C(4, 3) = 4
Probability:
The probability of an event occurring is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability that all three balls pulled out are red is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4 / 1320
Simplifying the fraction, we get:
Probability = 1 / 330
Therefore, the correct answer is option B) 1/55.
Four red balls, four green balls, and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all three balls are red is:
Solution:
To find the probability that all three balls pulled out are red, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When three balls are pulled out one after another without replacement, the total number of outcomes can be calculated using the concept of permutations. Since there are twelve balls in total, the first ball can be any of the twelve, the second ball can be any of the remaining eleven, and the third ball can be any of the remaining ten. Therefore, the total number of outcomes is:
Total outcomes = 12 * 11 * 10 = 1320
Number of favorable outcomes:
Since we want all three balls to be red, we need to choose three red balls out of the four available. The number of ways to choose three red balls out of four is given by the combination formula:
Number of favorable outcomes = C(4, 3) = 4
Probability:
The probability of an event occurring is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability that all three balls pulled out are red is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4 / 1320
Simplifying the fraction, we get:
Probability = 1 / 330
Therefore, the correct answer is option B) 1/55.
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Four red balls, four green balls and four blue balls are put in a box. Three balls are pulledout of the box at random one after another without replacement. The probability thatall the three balls are red isa)1/72b)1/55c)1/36d)1/27Correct answer is option 'B'. Can you explain this answer?
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