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A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?
- a)3/30
- b)11/21
- c)5/18
- d)11/23
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at...
Total balls = 15
Not red means green or blue i.e. any of (5+6) = 11 balls
So prob. = 11C2 / 15C2
Not red means green or blue i.e. any of (5+6) = 11 balls
So prob. = 11C2 / 15C2
Most Upvoted Answer
A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at...
To find the probability of not drawing a red ball, we need to find the probability of drawing two balls that are either blue or green.
Total number of balls in the box = 6 blue + 5 green + 4 red = 15
Probability of drawing a blue ball on the first draw = 6 blue balls / 15 total balls = 2/5
Probability of drawing a green ball on the first draw = 5 green balls / 15 total balls = 1/3
Since we want to find the probability of not drawing a red ball, we can calculate this by finding the probability of drawing two balls that are either blue or green.
Probability of drawing a blue ball on the first draw and a green ball on the second draw:
= (6 blue balls / 15 total balls) * (5 green balls / 14 remaining balls)
= (2/5) * (5/14)
= 1/7
Probability of drawing a green ball on the first draw and a blue ball on the second draw:
= (5 green balls / 15 total balls) * (6 blue balls / 14 remaining balls)
= (1/3) * (6/14)
= 1/7
Therefore, the probability of drawing two balls that are either blue or green is 1/7 + 1/7 = 2/7.
Hence, the probability of not drawing a red ball is 2/7.
Since none of the given options have 2/7 as the answer, none of the options provided are correct.
Total number of balls in the box = 6 blue + 5 green + 4 red = 15
Probability of drawing a blue ball on the first draw = 6 blue balls / 15 total balls = 2/5
Probability of drawing a green ball on the first draw = 5 green balls / 15 total balls = 1/3
Since we want to find the probability of not drawing a red ball, we can calculate this by finding the probability of drawing two balls that are either blue or green.
Probability of drawing a blue ball on the first draw and a green ball on the second draw:
= (6 blue balls / 15 total balls) * (5 green balls / 14 remaining balls)
= (2/5) * (5/14)
= 1/7
Probability of drawing a green ball on the first draw and a blue ball on the second draw:
= (5 green balls / 15 total balls) * (6 blue balls / 14 remaining balls)
= (1/3) * (6/14)
= 1/7
Therefore, the probability of drawing two balls that are either blue or green is 1/7 + 1/7 = 2/7.
Hence, the probability of not drawing a red ball is 2/7.
Since none of the given options have 2/7 as the answer, none of the options provided are correct.
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