Question

Martin has a pencil case which contains 4 blue pens and 3 green pens. Martin picks a pen at random from the pencil case. He notes its colour, and then replaces it. He does this two more times. Work out the probability that when Martin takes three pens, exactly two are the same colour. (3 marks)

Answer 1

The probability that when Martin takes three pens, exactly two are the same color is 72/343.

Step-by-step explanation:

To find the probability that Martin takes three pens, exactly two are the same color, we need to consider two cases: two blue pens and one green pen, or two green pens and one blue pen. First, let's calculate the probability of selecting two blue pens and one green pen:

1. The probability of selecting a blue pen on the first draw is 4/7.
2. After replacing the pen, the probability of selecting another blue pen on the second draw is also 4/7.
3. The probability of selecting a green pen on the third draw is 3/7.

To calculate the probability of selecting two green pens and one blue pen, we can use the same steps as above, swapping the probabilities of blue and green.

Finally, we add the two probabilities together to get the total probability:
(4/7)*(4/7)*(3/7)+(3/7)*(3/7)*(4/7) = 72/343.