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A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour is
- a)1/36
- b)1/6
- c)1/4
- d)1/3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A...
The given condition corresponds to sampling with replacement and with order.
No 2 marbles have the same color i.e. Drawn 3 different marble.
So total number of ways for picking 3 different marbles = 3! = 6.
Probability of getting blue, green, red in order
[Since 6 ways to get the marbles]
= 1/6
No 2 marbles have the same color i.e. Drawn 3 different marble.
So total number of ways for picking 3 different marbles = 3! = 6.
Probability of getting blue, green, red in order
[Since 6 ways to get the marbles]
= 1/6
Most Upvoted Answer
A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A...
Problem Analysis:
To solve this problem, we need to find the probability that no two marbles drawn have the same color.
Given:
- Blue marbles: 10
- Green marbles: 20
- Red marbles: 30
- Total marbles: 10+20+30=60
- Number of draws: 3
Solution:
To find the probability of no two marbles having the same color, we need to consider two cases:
1. Drawing three different colored marbles
2. Drawing two different colored marbles
Case 1: Drawing three different colored marbles
In this case, we need to calculate the probability of drawing three different colored marbles.
The probability of drawing a blue marble on the first draw is 10/60 = 1/6.
After putting the marble back in the bag, the probability of drawing a green marble on the second draw is 20/60 = 1/3.
Similarly, the probability of drawing a red marble on the third draw is 30/60 = 1/2.
Since these events are independent, we can multiply the probabilities to get the overall probability of drawing three different colored marbles:
P(3 different colors) = (1/6) * (1/3) * (1/2) = 1/36
Case 2: Drawing two different colored marbles
In this case, we need to calculate the probability of drawing two different colored marbles and one marble of the same color.
There are three possibilities for this case:
a) Drawing two blue marbles and one green marble
b) Drawing two blue marbles and one red marble
c) Drawing two green marbles and one red marble
Sub-case a: Drawing two blue marbles and one green marble
The probability of drawing a blue marble on the first draw is 10/60 = 1/6.
After putting the marble back in the bag, the probability of drawing another blue marble on the second draw is also 1/6.
Finally, the probability of drawing a green marble on the third draw is 20/60 = 1/3.
So, the overall probability of this sub-case is:
P(2 blue, 1 green) = (1/6) * (1/6) * (1/3) = 1/108
Sub-case b: Drawing two blue marbles and one red marble
The probability of drawing a blue marble on the first draw is 1/6.
After putting the marble back in the bag, the probability of drawing another blue marble on the second draw is also 1/6.
Finally, the probability of drawing a red marble on the third draw is 30/60 = 1/2.
So, the overall probability of this sub-case is:
P(2 blue, 1 red) = (1/6) * (1/6) * (1/2) = 1/72
Sub-case c: Drawing two green marbles and one red marble
The probability of drawing a green marble on the first draw is 20/60 = 1/3.
After putting the marble back in the bag, the probability of drawing another green marble on the
To solve this problem, we need to find the probability that no two marbles drawn have the same color.
Given:
- Blue marbles: 10
- Green marbles: 20
- Red marbles: 30
- Total marbles: 10+20+30=60
- Number of draws: 3
Solution:
To find the probability of no two marbles having the same color, we need to consider two cases:
1. Drawing three different colored marbles
2. Drawing two different colored marbles
Case 1: Drawing three different colored marbles
In this case, we need to calculate the probability of drawing three different colored marbles.
The probability of drawing a blue marble on the first draw is 10/60 = 1/6.
After putting the marble back in the bag, the probability of drawing a green marble on the second draw is 20/60 = 1/3.
Similarly, the probability of drawing a red marble on the third draw is 30/60 = 1/2.
Since these events are independent, we can multiply the probabilities to get the overall probability of drawing three different colored marbles:
P(3 different colors) = (1/6) * (1/3) * (1/2) = 1/36
Case 2: Drawing two different colored marbles
In this case, we need to calculate the probability of drawing two different colored marbles and one marble of the same color.
There are three possibilities for this case:
a) Drawing two blue marbles and one green marble
b) Drawing two blue marbles and one red marble
c) Drawing two green marbles and one red marble
Sub-case a: Drawing two blue marbles and one green marble
The probability of drawing a blue marble on the first draw is 10/60 = 1/6.
After putting the marble back in the bag, the probability of drawing another blue marble on the second draw is also 1/6.
Finally, the probability of drawing a green marble on the third draw is 20/60 = 1/3.
So, the overall probability of this sub-case is:
P(2 blue, 1 green) = (1/6) * (1/6) * (1/3) = 1/108
Sub-case b: Drawing two blue marbles and one red marble
The probability of drawing a blue marble on the first draw is 1/6.
After putting the marble back in the bag, the probability of drawing another blue marble on the second draw is also 1/6.
Finally, the probability of drawing a red marble on the third draw is 30/60 = 1/2.
So, the overall probability of this sub-case is:
P(2 blue, 1 red) = (1/6) * (1/6) * (1/2) = 1/72
Sub-case c: Drawing two green marbles and one red marble
The probability of drawing a green marble on the first draw is 20/60 = 1/3.
After putting the marble back in the bag, the probability of drawing another green marble on the
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A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour isa)1/36b)1/6c)1/4d)1/3Correct answer is option 'B'. Can you explain this answer?
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A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour isa)1/36b)1/6c)1/4d)1/3Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour isa)1/36b)1/6c)1/4d)1/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour isa)1/36b)1/6c)1/4d)1/3Correct answer is option 'B'. Can you explain this answer?.
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