A container has three white balls and two red balls. A first ball is drawn at random and not replaces. Then a second ball is drawn. give the following conditions. What is the probability that the second ball was red? The first ball was white? The first ball was red?

1. First ball was red

No. of red balls: 2
Total number of balls:5
P(R)=2/5
2. First ball was white
No. of white balls: 3
Total number of balls: 5
P(W)=3/5
3. Second ball was red:
The probability is given by
P(R,R)+P(W,R)

Now we'll calculate P(R,R)
P(R)=2/5
After the first red, there is one more red left, and four balls altogether, therefore
P(RR)=(2/5)*(1/4)
=1/10
Similarly,
P(WR)=(3/5)*(2/4)
=3/10
Probability of the second ball being red is
(1/10)+(3/10)
=2/5

To calculate the probabilities, we need to consider the possible outcomes and their probabilities for each condition.

Let's start with the probability that the second ball drawn is red. Given that the first ball was drawn and not replaced, there are two scenarios that lead to a red ball being drawn second.

Scenario 1: The first ball is red, which leaves only one red ball remaining in the container. The probability of drawing a red ball in this scenario is 1/2.

Scenario 2: The first ball is white, which leaves two red balls remaining in the container. The probability of drawing a red ball in this scenario is 2/3.

To calculate the overall probability for the second ball being red, we need to consider the probabilities of both scenarios and add them together.

Probability (second ball is red) = Probability (first ball is red) * Probability (second ball is red | first ball is red)
+ Probability (first ball is white) * Probability (second ball is red | first ball is white)
= (2/5)*(1/2) + (3/5)*(2/3)
= 2/10 + 6/15
= 1/5 + 2/5
= 3/5
≈ 0.6
Therefore, the probability that the second ball drawn is red is approximately 0.6 or 60%.

Next, let's calculate the probability that the first ball drawn is white. Since there are three white balls in the container, the probability of drawing a white ball as the first ball is simply 3/5 or 60%.

Finally, let's calculate the probability that the first ball drawn is red. Given that there are two red balls in the container, the probability of drawing a red ball as the first ball is 2/5 or 40%.

To summarize:
- Probability (second ball is red) = 3/5 or 60%
- Probability (first ball is white) = 3/5 or 60%
- Probability (first ball is red) = 2/5 or 40%