Question

There is a bag filled with 3 blue, 4 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?

Answer 1

ANSWER -

Calculate Total marbles

Total marbles = Blue + Red + Green

Total marbles = 3 + 4 + 5

Total marbles = 12

Probability of a green = 5/12

Probability of not green = 1 - 5/12 = 7/12

To get exactly one green in two draws, we either get a green, not green, or a not green, green

First Draw Green, Second Draw Not Green

1st draw: Probability of a green = 5/12

2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

Probability of the event is (5/12) * (7/11) = 35/132

First Draw Not Green, Second Draw Not Green

1st draw: Probability of not a green = 7/12

2nd draw: Probability of not green = 5/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

Probability of the event is (7/12) * (5/11) = 35/132

To get the probability of exactly one green, we add both of the events:

First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green

35/132 + 35/132 = 70/132

SO THE ANS IS 35/66...

Hope that this will helpful to u...

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Answer 2

Answer:

The probability of getting 2 different colours is 0.653.

Step-by-step explanation:

Total marbles = 3 blue + 4 red + 5 green

Total marbles = 12

Probability of a green = 5 / 12

Probability of not green = 1 - 5 / 12 = 7 / 12

Probability of a red = 4 / 12

Probability of not red = 1 - 4 / 12 = 8 / 12

Probability of a blue = 3 / 12

Probability of not blue = 1 - 3 / 12 = 9 / 12

Now,

Case 1: In first draw, we get green and in second draw, we get not green:

P ( Case 1 ) = 5 / 12 × 7 / 12 = 35 / 144

Case 2: In first draw, we get red and in second draw, we get not red:

P ( Case 2 ) = 4 / 12 × 8 / 12 = 32 / 144

Case 3: In first draw, we get blue and in second draw, we get not blue:

P ( Case 3 ) = 3 / 12 × 9 / 12 = 27 / 144

The probability of getting 2 different colours:

P ( different colours) = 35 / 144 + 32 / 144 + 27 / 144

P = 94 / 144 = 47 / 72

P = 0.653

Therefore, the probability of getting 2 different colours is 0.653.

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