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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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A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A...
Problem:
A bag contains 10 blue marbles, 20 green marbles, and 30 red marbles. A marble is drawn from the bag, its color 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 color is:
a) 1/36
b) 1/6
c) 1/4
d) 1/3
Explanation:
To solve this problem, we need to calculate the probability of selecting three marbles of different colors out of the total marbles in the bag. Let's break down the problem into steps:
Step 1: Calculate the probability of selecting a blue marble:
The bag contains a total of 60 marbles (10 blue + 20 green + 30 red). The probability of selecting a blue marble on the first draw is:
P(blue) = 10/60 = 1/6
Step 2: Calculate the probability of selecting a green marble:
After the first draw, the bag still contains 60 marbles, but now there are 9 blue marbles left. The probability of selecting a green marble on the second draw is:
P(green) = 20/60 = 1/3
Step 3: Calculate the probability of selecting a red marble:
After the second draw, there are 8 blue marbles and 19 green marbles left in the bag. The probability of selecting a red marble on the third draw is:
P(red) = 30/60 = 1/2
Step 4: Calculate the probability of selecting marbles of different colors:
To find the probability of selecting marbles of different colors in all three draws, we multiply the probabilities from each step together:
P(different colors) = P(blue) * P(green) * P(red)
= (1/6) * (1/3) * (1/2)
= 1/36
Therefore, the probability that no two of the marbles drawn have the same color is 1/36, which corresponds to option (a).
A bag contains 10 blue marbles, 20 green marbles, and 30 red marbles. A marble is drawn from the bag, its color 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 color is:
a) 1/36
b) 1/6
c) 1/4
d) 1/3
Explanation:
To solve this problem, we need to calculate the probability of selecting three marbles of different colors out of the total marbles in the bag. Let's break down the problem into steps:
Step 1: Calculate the probability of selecting a blue marble:
The bag contains a total of 60 marbles (10 blue + 20 green + 30 red). The probability of selecting a blue marble on the first draw is:
P(blue) = 10/60 = 1/6
Step 2: Calculate the probability of selecting a green marble:
After the first draw, the bag still contains 60 marbles, but now there are 9 blue marbles left. The probability of selecting a green marble on the second draw is:
P(green) = 20/60 = 1/3
Step 3: Calculate the probability of selecting a red marble:
After the second draw, there are 8 blue marbles and 19 green marbles left in the bag. The probability of selecting a red marble on the third draw is:
P(red) = 30/60 = 1/2
Step 4: Calculate the probability of selecting marbles of different colors:
To find the probability of selecting marbles of different colors in all three draws, we multiply the probabilities from each step together:
P(different colors) = P(blue) * P(green) * P(red)
= (1/6) * (1/3) * (1/2)
= 1/36
Therefore, the probability that no two of the marbles drawn have the same color is 1/36, which corresponds to option (a).
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Community 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
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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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