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A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are green?
- a)1/78
- b)2/75
- c)4/89
- d)None
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked ...
13C2 = 13*12/2 =78
2C2 = 1
P = 1/78
2C2 = 1
P = 1/78
Most Upvoted Answer
A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked ...
To find the probability of picking two green balls from the bag, we need to consider the total number of outcomes and the favorable outcomes.
Total Number of Balls
- Red balls: 6
- Blue balls: 5
- Green balls: 2
Total Number of Balls in the Bag = 6 (red) + 5 (blue) + 2 (green) = 13
Total Number of Outcomes
When two balls are picked at random, there are a total of (13 choose 2) possible outcomes. This can be calculated using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen.
(13 choose 2) = 13! / (2!(13-2)!)
= (13 * 12) / (2 * 1)
= 78
Favorable Outcomes
To get two green balls, we need to pick both green balls from the bag. There are 2 green balls in the bag, so the number of favorable outcomes is (2 choose 2) = 1.
Probability Calculation
The probability of an event is given by the ratio of favorable outcomes to total outcomes.
Probability of picking two green balls = (Number of favorable outcomes) / (Total number of outcomes)
= 1 / 78
Therefore, the correct answer is option 'A': 1/78.
Total Number of Balls
- Red balls: 6
- Blue balls: 5
- Green balls: 2
Total Number of Balls in the Bag = 6 (red) + 5 (blue) + 2 (green) = 13
Total Number of Outcomes
When two balls are picked at random, there are a total of (13 choose 2) possible outcomes. This can be calculated using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen.
(13 choose 2) = 13! / (2!(13-2)!)
= (13 * 12) / (2 * 1)
= 78
Favorable Outcomes
To get two green balls, we need to pick both green balls from the bag. There are 2 green balls in the bag, so the number of favorable outcomes is (2 choose 2) = 1.
Probability Calculation
The probability of an event is given by the ratio of favorable outcomes to total outcomes.
Probability of picking two green balls = (Number of favorable outcomes) / (Total number of outcomes)
= 1 / 78
Therefore, the correct answer is option 'A': 1/78.
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A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are green?a)1/78b)2/75c)4/89d)NoneCorrect answer is option 'A'. Can you explain this answer?
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