Monique has a box that contains the following marbles: 5 yellow marbles, 3 green marbles, 2 orange marbles. She randomly selects 2 marbles from the box and keeps them. If she randomly selects a third marble from the box, the probability that she selects a green marble will be 2/10. Which of the following statements could be true about the first two marbles she selected.
a. 1 yellow and 1 green
b. 1 orange and 1 yellow
c. 1 orange and 1 blue
d. both were green
e. both were blue
To find the probability that Monique selects a green marble on her third selection, we need to consider the scenarios in which this can occur.
Let's look at the possible scenarios for the first two marbles Monique selects:
a. 1 yellow and 1 green: In this scenario, Monique has already selected a green marble, so the probability of selecting another green marble on her third selection will be 1/9, not 2/10. Therefore, option a is not possible.
b. 1 orange and 1 yellow: In this scenario, Monique has not selected any green marbles yet. Thus, the probability of selecting a green marble on her third selection is 3/9 (since there are 3 green marbles remaining out of 9 marbles). This is not equal to 2/10, so option b is also not possible.
c. 1 orange and 1 blue: This option includes a blue marble, which was not mentioned in the given box's contents. So option c is not possible.
d. Both were green: In this scenario, Monique has already selected 2 green marbles, which matches the condition mentioned in the question. Therefore, option d is a possible answer.
e. Both were blue: Similarly, this option includes a blue marble that was not mentioned in the given box's contents. Hence, option e is not possible.
Therefore, the only possible statement about the first two marbles Monique selected is that both of them were green (option d).