Mechanical Engineering Exam > Mechanical Engineering Questions > A box contains 5 black and 5 red balls. Two b...
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A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability of both balls being red is
- a)2/9
- b)1/5
- c)19/90
- d)1/90
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A box contains 5 black and 5 red balls. Two balls are randomly picked ...
Problem:
A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability of both balls being red is:
Solution:
To find the probability of both balls being red, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When two balls are picked from the box without replacement, the total number of outcomes can be determined using the concept of combinations. The total number of ways to choose 2 balls out of 10 is given by the combination formula:
nCr = n! / (r!(n-r)!)
Here, n = 10 (total number of balls in the box) and r = 2 (number of balls to be picked). Substituting the values, we get:
10C2 = 10! / (2!(10-2)!) = 45
So, there are 45 possible outcomes when two balls are picked from the box without replacement.
Number of Favorable Outcomes:
The number of favorable outcomes is the number of ways to choose 2 red balls out of the 5 red balls in the box. Again, using the combination formula:
5C2 = 5! / (2!(5-2)!) = 10
So, there are 10 favorable outcomes.
Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability of both balls being red is:
P(both balls red) = (Number of favorable outcomes) / (Total number of outcomes)
= 10 / 45
= 2/9
Hence, the correct answer is option 'A' i.e., the probability of both balls being red is 2/9.
A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability of both balls being red is:
Solution:
To find the probability of both balls being red, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When two balls are picked from the box without replacement, the total number of outcomes can be determined using the concept of combinations. The total number of ways to choose 2 balls out of 10 is given by the combination formula:
nCr = n! / (r!(n-r)!)
Here, n = 10 (total number of balls in the box) and r = 2 (number of balls to be picked). Substituting the values, we get:
10C2 = 10! / (2!(10-2)!) = 45
So, there are 45 possible outcomes when two balls are picked from the box without replacement.
Number of Favorable Outcomes:
The number of favorable outcomes is the number of ways to choose 2 red balls out of the 5 red balls in the box. Again, using the combination formula:
5C2 = 5! / (2!(5-2)!) = 10
So, there are 10 favorable outcomes.
Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability of both balls being red is:
P(both balls red) = (Number of favorable outcomes) / (Total number of outcomes)
= 10 / 45
= 2/9
Hence, the correct answer is option 'A' i.e., the probability of both balls being red is 2/9.
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Community Answer
A box contains 5 black and 5 red balls. Two balls are randomly picked ...
Given:
Black balls = 5, Red balls = 5, Total balls = 10
Here, two balls are picked from the box randomly, one after the other without replacement. So, the probability of both the balls being red is:
Black balls = 5, Red balls = 5, Total balls = 10
Here, two balls are picked from the box randomly, one after the other without replacement. So, the probability of both the balls being red is:
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A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability of both balls being red isa)2/9b)1/5c)19/90d)1/90Correct answer is option 'A'. Can you explain this answer?
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