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A bag contains 6 red balls and 8 green balls. 2 balls are drawn at random one by one with replacement. Find the probability that both the balls are green
- a)16/49
- b)25/49
- c)12/49
- d)21/49
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A bag contains 6 red balls and 8 green balls. 2 balls are drawn at ran...
(8c1)/(14c1) * (8c1)*(14c1) = 16/49
Most Upvoted Answer
A bag contains 6 red balls and 8 green balls. 2 balls are drawn at ran...
Solution:
Given:
Number of red balls = 6
Number of green balls = 8
Two balls are drawn at random one by one with replacement.
To find: Probability that both the balls are green.
Let's solve this by applying the formula of probability.
Formula: Probability of an event happening = Number of ways an event can happen/Total number of outcomes
Total number of outcomes = 14 × 14 = 196 (as we are drawing two balls with replacement)
Number of ways of drawing a green ball on first draw = 8/14 = 4/7
Number of ways of drawing a green ball on second draw = 8/14 = 4/7
As the draws are independent, we can multiply the probabilities of both the events.
Therefore, the probability of drawing two green balls = Number of ways of drawing two green balls/Total number of outcomes
Number of ways of drawing two green balls = 4/7 × 4/7 = 16/49
Therefore, the probability that both the balls are green is 16/49.
Hence, option (a) is the correct answer.
Given:
Number of red balls = 6
Number of green balls = 8
Two balls are drawn at random one by one with replacement.
To find: Probability that both the balls are green.
Let's solve this by applying the formula of probability.
Formula: Probability of an event happening = Number of ways an event can happen/Total number of outcomes
Total number of outcomes = 14 × 14 = 196 (as we are drawing two balls with replacement)
Number of ways of drawing a green ball on first draw = 8/14 = 4/7
Number of ways of drawing a green ball on second draw = 8/14 = 4/7
As the draws are independent, we can multiply the probabilities of both the events.
Therefore, the probability of drawing two green balls = Number of ways of drawing two green balls/Total number of outcomes
Number of ways of drawing two green balls = 4/7 × 4/7 = 16/49
Therefore, the probability that both the balls are green is 16/49.
Hence, option (a) is the correct answer.
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