To find the probability that both pens are the same color, we need to consider the different possible scenarios.
Scenario 1: Gary first takes a red pen and then another red pen.
The probability of the first event is 5/10 (5 red pens out of 10 total pens).
After the first event, there are 4 red pens and a total of 9 pens remaining, so the probability of the second event is 4/9.
Therefore, the probability of this scenario is (5/10) * (4/9) = 20/90.
Scenario 2: Gary first takes a blue pen and then another blue pen.
The probability of the first event is 3/10 (3 blue pens out of 10 total pens).
After the first event, there are 2 blue pens and a total of 9 pens remaining, so the probability of the second event is 2/9.
Therefore, the probability of this scenario is (3/10) * (2/9) = 6/90.
Scenario 3: Gary first takes a green pen and then another green pen.
The probability of the first event is 2/10 (2 green pens out of 10 total pens).
After the first event, there is 1 green pen and a total of 9 pens remaining, so the probability of the second event is 1/9.
Therefore, the probability of this scenario is (2/10) * (1/9) = 2/90.
Adding up the probabilities of the three scenarios, we get: (20/90) + (6/90) + (2/90) = 28/90.
Therefore, the probability that both pens are the same color is 28/90, which simplifies to 14/45.
There are 5 red pens, 3 blue pens and 2 green pens in a box. Gary takes at random a pen from the box and gives the pen to his friend. He then takes at random another pen the box. What's the probability that both pens are the same colour?
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