Question

There is a bag filled with 6 blue and 5 red 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 of the same colour?

Answer 1

Answer: 61/121

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Work Shown:

B = event of getting a blue marble

R = event of getting a red marble

P(B) = (6 blue)/(6+5 total) = 6/11

P(R) = (5 red)/(11 total) = 5/11

P(2 blue) = P(B)*P(B) = (6/11)*(6/11) = 36/121

P(2 red) = P(R)*P(R) = (5/11)*(5/11) = 25/121

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P(2 same color) = P(2 blue OR 2 red)

P(2 same color) = P(2 blue) + P(2 red)

P(2 same color) = 36/121 + 25/121

P(2 same color) = (36+25)/121

P(2 same color) = 61/121

Answer 2

25/121

Explanation:

This is called sampling with replacement.

The probability of getting a red marble in one sample is 5/11. Since you are sampling twice, the probability of picking a red marble both times is 5/11 X 5/11 = 25/121. That is slightly less than ⅕.