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A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random form the bag. The probability that all of them are red is:
- a)2/91
- b)3/22
- c)1/22
- d)2/77
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn ...
Total balls in the bag are = 15
Sample space = 15c3
The probability that all the balls are red is
Sample space = 15c3
The probability that all the balls are red is
Most Upvoted Answer
A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn ...
Problem:
A bag contains 4 white, 5 red, and 6 blue balls. Three balls are drawn at random from the bag. Find the probability that all three balls are red.
Solution:
To find the probability that all three balls drawn are red, we need to find the total number of favorable outcomes (drawing three red balls) and divide it by the total number of possible outcomes (drawing any three balls).
Total Number of Balls:
The bag contains a total of 4 white + 5 red + 6 blue = 15 balls.
Total Number of Possible Outcomes:
When we draw three balls from the bag, the total number of possible outcomes can be calculated using the concept of combinations. We can choose 3 balls out of the 15 balls in the bag in C(15, 3) ways.
C(n, r) represents the number of combinations of n items taken r at a time and can be calculated using the formula:
C(n, r) = n! / (r! * (n-r)!)
In our case, C(15, 3) = 15! / (3! * (15-3)!) = 15! / (3! * 12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455
Therefore, the total number of possible outcomes is 455.
Total Number of Favorable Outcomes:
Since we want to draw all three balls as red, we can choose 3 red balls out of the 5 red balls in the bag in C(5, 3) ways.
C(5, 3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4) / (2 * 1) = 10
Therefore, the total number of favorable outcomes is 10.
Probability:
The probability that all three balls drawn are red is given by the ratio of the total number of favorable outcomes to the total number of possible outcomes.
Probability = (Total Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
= 10 / 455
= 2 / 91
Hence, the correct answer is option 'A' - 2/91.
A bag contains 4 white, 5 red, and 6 blue balls. Three balls are drawn at random from the bag. Find the probability that all three balls are red.
Solution:
To find the probability that all three balls drawn are red, we need to find the total number of favorable outcomes (drawing three red balls) and divide it by the total number of possible outcomes (drawing any three balls).
Total Number of Balls:
The bag contains a total of 4 white + 5 red + 6 blue = 15 balls.
Total Number of Possible Outcomes:
When we draw three balls from the bag, the total number of possible outcomes can be calculated using the concept of combinations. We can choose 3 balls out of the 15 balls in the bag in C(15, 3) ways.
C(n, r) represents the number of combinations of n items taken r at a time and can be calculated using the formula:
C(n, r) = n! / (r! * (n-r)!)
In our case, C(15, 3) = 15! / (3! * (15-3)!) = 15! / (3! * 12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455
Therefore, the total number of possible outcomes is 455.
Total Number of Favorable Outcomes:
Since we want to draw all three balls as red, we can choose 3 red balls out of the 5 red balls in the bag in C(5, 3) ways.
C(5, 3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4) / (2 * 1) = 10
Therefore, the total number of favorable outcomes is 10.
Probability:
The probability that all three balls drawn are red is given by the ratio of the total number of favorable outcomes to the total number of possible outcomes.
Probability = (Total Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
= 10 / 455
= 2 / 91
Hence, the correct answer is option 'A' - 2/91.
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A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random form the bag. The probability that all of them are red is:a)2/91b)3/22c)1/22d)2/77Correct answer is option 'A'. Can you explain this answer?
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