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There are 4 orange balls, 5 blue balls and 3 white balls are there in a bag. Two balls are selected at random. What is the probability of getting both the balls being blue?
- a)5/33
- b)3/33
- c)3/11
- d)3/5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
There are 4 orange balls, 5 blue balls and 3 white balls are there in ...
To find the probability of getting both balls being blue, we need to find the number of favorable outcomes (selecting 2 blue balls) and divide it by the total number of possible outcomes (selecting any 2 balls from the bag).
Favorable Outcomes:
We have 5 blue balls in the bag. When we select the first ball, there are 5 blue balls out of a total of 12 balls (4 orange + 5 blue + 3 white). After selecting the first blue ball, we have 4 blue balls left out of a total of 11 remaining balls. Therefore, the number of favorable outcomes is 5 * 4 = 20.
Total Possible Outcomes:
To find the total number of possible outcomes, we need to calculate the number of ways to select 2 balls out of 12. This can be done using the combination formula, which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.
In this case, n = 12 (total number of balls) and r = 2 (number of balls to be selected). Plugging in these values, we get:
12C2 = 12! / (2!(12-2)!)= 12! / (2! * 10!) = (12 * 11) / (2 * 1) = 66.
Probability:
The probability of getting both balls being blue is given by the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 20 / 66
Probability = 5 / 33
Therefore, the correct answer is option A) 5/33.
Favorable Outcomes:
We have 5 blue balls in the bag. When we select the first ball, there are 5 blue balls out of a total of 12 balls (4 orange + 5 blue + 3 white). After selecting the first blue ball, we have 4 blue balls left out of a total of 11 remaining balls. Therefore, the number of favorable outcomes is 5 * 4 = 20.
Total Possible Outcomes:
To find the total number of possible outcomes, we need to calculate the number of ways to select 2 balls out of 12. This can be done using the combination formula, which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.
In this case, n = 12 (total number of balls) and r = 2 (number of balls to be selected). Plugging in these values, we get:
12C2 = 12! / (2!(12-2)!)= 12! / (2! * 10!) = (12 * 11) / (2 * 1) = 66.
Probability:
The probability of getting both balls being blue is given by the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 20 / 66
Probability = 5 / 33
Therefore, the correct answer is option A) 5/33.
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Community Answer
There are 4 orange balls, 5 blue balls and 3 white balls are there in ...
Getting both blue 5/12 * 4/11 = 5/33
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