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A box contains 15 red marbles, 15 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that atleast one will be green?
- a)
- b)
- c)zero
- d)1
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A box contains 15 red marbles, 15 blue marbles and 30 green marbles. 5...
It's like doing the question orally... (don't get into maths... as I was also stuck in the middle) but by common sense (which is very uncommon) it can be said as 1-probablity of not getting any green in 5 balls... in this case we can see the answer aproaches to 1 which can be seen in option a) .... hope it helps... but with maths a can see a nightmare coming...
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Community Answer
A box contains 15 red marbles, 15 blue marbles and 30 green marbles. 5...
Calculation:
The total number of marbles in the box is 15 + 15 + 30 = 60.
Finding the probability:
To find the probability of drawing at least one green marble, we need to calculate the probability of the complement event (i.e., the event of not drawing any green marbles) and subtract it from 1.
Finding the probability of not drawing any green marbles:
The number of ways to choose 5 marbles out of the 60 marbles in the box is given by the binomial coefficient C(60, 5).
The number of ways to choose 5 marbles without any green marbles is given by the binomial coefficient C(45, 5) because we are only choosing from the 15 red marbles and 15 blue marbles.
Therefore, the probability of not drawing any green marbles is C(45, 5) / C(60, 5).
Finding the probability of drawing at least one green marble:
Now, we can calculate the probability of drawing at least one green marble by subtracting the probability of not drawing any green marbles from 1.
Probability of drawing at least one green marble = 1 - (C(45, 5) / C(60, 5))
Simplifying the expression:
C(45, 5) = (45*44*43*42*41) / (5*4*3*2*1)
C(60, 5) = (60*59*58*57*56) / (5*4*3*2*1)
Substituting these values into the expression:
Probability of drawing at least one green marble = 1 - [(45*44*43*42*41) / (60*59*58*57*56)]
Calculating the expression gives us the answer as 4367/4484.
Therefore, the probability that at least one marble drawn will be green is 4367/4484, which is option A.
The total number of marbles in the box is 15 + 15 + 30 = 60.
Finding the probability:
To find the probability of drawing at least one green marble, we need to calculate the probability of the complement event (i.e., the event of not drawing any green marbles) and subtract it from 1.
Finding the probability of not drawing any green marbles:
The number of ways to choose 5 marbles out of the 60 marbles in the box is given by the binomial coefficient C(60, 5).
The number of ways to choose 5 marbles without any green marbles is given by the binomial coefficient C(45, 5) because we are only choosing from the 15 red marbles and 15 blue marbles.
Therefore, the probability of not drawing any green marbles is C(45, 5) / C(60, 5).
Finding the probability of drawing at least one green marble:
Now, we can calculate the probability of drawing at least one green marble by subtracting the probability of not drawing any green marbles from 1.
Probability of drawing at least one green marble = 1 - (C(45, 5) / C(60, 5))
Simplifying the expression:
C(45, 5) = (45*44*43*42*41) / (5*4*3*2*1)
C(60, 5) = (60*59*58*57*56) / (5*4*3*2*1)
Substituting these values into the expression:
Probability of drawing at least one green marble = 1 - [(45*44*43*42*41) / (60*59*58*57*56)]
Calculating the expression gives us the answer as 4367/4484.
Therefore, the probability that at least one marble drawn will be green is 4367/4484, which is option A.
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A box contains 15 red marbles, 15 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that atleast one will be green?a)b)c)zerod)1Correct answer is option 'A'. Can you explain this answer?
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