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There are 3 red balls and 5 green balls in a bag. If two balls are picked at random from the bag then find the probability of getting a red ball?
- a)5/18
- b)4/19
- c)5/7
- d)15/28
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
There are 3 red balls and 5 green balls in a bag. If two balls are pic...
Required probability
=3C1*5C1/8C2
= 3*5/28
= 15/28
=3C1*5C1/8C2
= 3*5/28
= 15/28
Most Upvoted Answer
There are 3 red balls and 5 green balls in a bag. If two balls are pic...
Probability of getting a red ball from the bag can be determined by dividing the number of favorable outcomes by the total number of possible outcomes.
- Number of favorable outcomes: There are 3 red balls in the bag, so if we pick 2 balls, the number of ways to choose 1 red ball would be the number of ways to choose 1 ball out of the 3 red balls. This can be calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of balls and k is the number of balls to be chosen. In this case, n = 3 and k = 1, so there are C(3, 1) = 3 ways to choose 1 red ball.
- Total number of possible outcomes: There are a total of 8 balls in the bag (3 red + 5 green), so if we pick 2 balls, the number of ways to choose 2 balls out of the 8 balls can be calculated using the combination formula. In this case, n = 8 and k = 2, so there are C(8, 2) = 28 ways to choose 2 balls.
- Therefore, the probability of getting a red ball is the number of favorable outcomes divided by the total number of possible outcomes: 3/28.
- Simplifying the fraction, we get 1/9.
- However, the options given in the question do not include 1/9. So, let's check which option is the closest to 1/9.
- 5/18 is greater than 1/9, so it is not the correct answer.
- 4/19 is less than 1/9, so it is not the correct answer.
- 5/7 is greater than 1/9, so it is not the correct answer.
- 15/28 is the closest option to 1/9, so it is the correct answer.
Therefore, the probability of getting a red ball is 15/28, which is option 'D'.
- Number of favorable outcomes: There are 3 red balls in the bag, so if we pick 2 balls, the number of ways to choose 1 red ball would be the number of ways to choose 1 ball out of the 3 red balls. This can be calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of balls and k is the number of balls to be chosen. In this case, n = 3 and k = 1, so there are C(3, 1) = 3 ways to choose 1 red ball.
- Total number of possible outcomes: There are a total of 8 balls in the bag (3 red + 5 green), so if we pick 2 balls, the number of ways to choose 2 balls out of the 8 balls can be calculated using the combination formula. In this case, n = 8 and k = 2, so there are C(8, 2) = 28 ways to choose 2 balls.
- Therefore, the probability of getting a red ball is the number of favorable outcomes divided by the total number of possible outcomes: 3/28.
- Simplifying the fraction, we get 1/9.
- However, the options given in the question do not include 1/9. So, let's check which option is the closest to 1/9.
- 5/18 is greater than 1/9, so it is not the correct answer.
- 4/19 is less than 1/9, so it is not the correct answer.
- 5/7 is greater than 1/9, so it is not the correct answer.
- 15/28 is the closest option to 1/9, so it is the correct answer.
Therefore, the probability of getting a red ball is 15/28, which is option 'D'.
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There are 3 red balls and 5 green balls in a bag. If two balls are picked at random from the bag then find the probability of getting a red ball?a)5/18b)4/19c)5/7d)15/28Correct answer is option 'D'. Can you explain this answer?
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