there are 3 red marbles , 3 blue marbles and 1 green marble in a bag. A marble is drawn at random from the bag and not replaced. Then a second marble is drawn. What are all the possible outcomes?
To determine all the possible outcomes, we need to consider all the different combinations of marbles that can be drawn.
In this case, we have three different types of marbles: red, blue, and green. Let's denote them as R, B, and G, respectively.
The total number of marbles in the bag is 3 (red) + 3 (blue) + 1 (green) = 7.
When the first marble is drawn, there are a total of 7 possible outcomes. Let's list them:
1) R - If the first marble drawn is red.
2) R - If the first marble drawn is red.
3) R - If the first marble drawn is red.
4) B - If the first marble drawn is blue.
5) B - If the first marble drawn is blue.
6) B - If the first marble drawn is blue.
7) G - If the first marble drawn is green.
Now, let's consider the second marble that is drawn. Since we didn't replace the first marble, the number of remaining marbles changes based on the first marble drawn.
If the first marble drawn was red, we have 2 remaining red marbles, 3 blue marbles, and 1 green marble in the bag.
If the first marble drawn was blue, we have 3 red marbles, 2 remaining blue marbles, and 1 green marble in the bag.
If the first marble drawn was green, we have 3 red marbles, 3 blue marbles, and 0 remaining green marbles in the bag.
Taking into account these different scenarios, let's list all the possible outcomes of the second marble being drawn:
If the first marble drawn was red:
1) RR - If the second marble drawn is red.
2) RB - If the second marble drawn is blue.
3) RG - If the second marble drawn is green.
If the first marble drawn was blue:
4) BR - If the second marble drawn is red.
5) BB - If the second marble drawn is blue.
6) BG - If the second marble drawn is green.
If the first marble drawn was green:
7) GR - If the second marble drawn is red.
8) GB - If the second marble drawn is blue.
To summarize, the eight possible outcomes are:
1) RR
2) RB
3) RG
4) BR
5) BB
6) BG
7) GR
8) GB