A box contains three white balls and two red balls. A ball is drawn at random from the box and not replaced. Then a second ball is drawn from the box. Draw a tree diagram for this experiment and find the probability that the two balls are of different colors.

there are only 4 cases:

WW --- prob is (3/5)(2/4) = 6/20
WR --- prob is (3/5)(2/4) = 6/20
RW --- prob is (2/5)(3/4) = 6/20
RR --- prob is (2/5)(1/4) = 2/20

so different colours are : WR and RW = 6/20 + 6/20 = 12/20 = 3/5

(notice the 4 cases add up to 1)

To draw a tree diagram for this experiment, follow these steps:

Step 1: Draw a square on the left side of the page to represent the first draw.

Step 2: Inside the square, write "W" for a white ball and "R" for a red ball, indicating the possibilities.

Step 3: Draw two branches extending from the square to represent all possible outcomes for the second draw.

Step 4: On the first branch, write "R" if a red ball is drawn on the first draw and "W" if a white ball is drawn.

Step 5: On the second branch, write "R" if a red ball is drawn on the first draw and "R" if a red ball is drawn.

Step 6: Draw two branches extending from each branch in step 5 to represent all possible outcomes for the second draw.

Step 7: Repeat steps 4 to 6 for the branch in step 3.

Here is the tree diagram:

```
| First draw
|

W
|

R
/ \
▼ ▼
W R
/ \ / \
▼ ▼ ▼ ▼
R W W R

```

To find the probability that the two balls are of different colors, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Favorable outcomes: There are four favorable outcomes - (WR, RW, WR, RW).

Total outcomes: There are five possible outcomes - (WW, WR, RW, RR, RR).

Therefore, the probability of drawing two balls of different colors is 4/5, which can also be written as 0.8 or 80%.

To create a tree diagram for this experiment, we need to outline the possible outcomes at each stage of the process. Let's start by labeling the two stages:

Stage 1: Drawing the first ball
Stage 2: Drawing the second ball

Now, let's consider the possible outcomes at each stage:

Stage 1: Drawing the first ball
- Outcome A: White ball
- Outcome B: Red ball

Stage 2: Drawing the second ball
- Outcome A: White ball (if the first ball was white)
- Outcome B: Red ball (if the first ball was white)
- Outcome C: White ball (if the first ball was red)
- Outcome D: Red ball (if the first ball was red)

Now, we can construct the tree diagram:

|----- A: White ---- A: White
|
|----- A: White ---- B: Red
|
|----- B: Red ---- C: White
|
|----- B: Red ---- D: Red

To find the probability that the two balls are of different colors, we need to determine the total number of outcomes where two balls of different colors are drawn. In this case, we need to consider the outcomes B: Red ---- C: White and B: Red ---- D: Red.

The probability of drawing a red ball as the first outcome is 2/5 (as there are two red balls out of a total of five).

After drawing a red ball, the probability of drawing a white ball is 3/4 (since we already removed one ball from the box).

So, the probability of drawing one red ball followed by one white ball is (2/5) * (3/4) = 6/20 or 3/10.

Next, we find the probability of drawing two red balls in a row, which is (2/5) * (1/4) = 2/20 or 1/10.

Now, we can add up the probabilities of these two outcomes:

Probability of drawing two balls of different colors = (3/10) + (1/10) = 4/10 or 2/5.

Therefore, the probability that the two balls drawn are of different colors is 2/5.