one bag contains 4 white balls,2 black balls.another bag contains 3 white balls 5 black balls.if one ball is drawn from each bag. find that

a) both are white?
b) both are black?
c)one is white and one is black?

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

a. 4/6 * 3/8 = ?

b. same process

c. Either-or probabilities are found by adding the individual probabilities.

4/6 * 5/8 + 2/6 * 3/8 = ?

To solve this problem, we can find the probability of each scenario by considering the number of total possible outcomes and the number of favorable outcomes for each case.

First, let's find the probabilities for each individual bag:

Bag 1:
- 4 white balls and 2 black balls
- Total possible outcomes = 4 + 2 = 6

Bag 2:
- 3 white balls and 5 black balls
- Total possible outcomes = 3 + 5 = 8

Now, let's calculate the probabilities for each scenario:

a) Both balls are white:
- Probability of drawing a white ball from Bag 1: 4/6 = 2/3
- Probability of drawing a white ball from Bag 2: 3/8
- Probability of both balls being white = (2/3) * (3/8) = 1/4

b) Both balls are black:
- Probability of drawing a black ball from Bag 1: 2/6 = 1/3
- Probability of drawing a black ball from Bag 2: 5/8
- Probability of both balls being black = (1/3) * (5/8) = 5/24

c) One is white and one is black:
To find this probability, we must consider two possibilities: either a white ball is drawn from Bag 1 and a black ball from Bag 2, or a white ball is drawn from Bag 2 and a black ball from Bag 1.

- Probability of drawing a white ball from Bag 1 and a black ball from Bag 2 = (4/6) * (5/8) = 5/12
- Probability of drawing a white ball from Bag 2 and a black ball from Bag 1 = (3/8) * (2/6) = 1/8

- Total probability of one white ball and one black ball = (5/12) + (1/8) = 11/24

Therefore:
a) The probability of both balls being white is 1/4.
b) The probability of both balls being black is 5/24.
c) The probability of one ball being white and the other being black is 11/24.