There are two containers, with one containing 4 Red and 3 Green balls and the other containing 3 Blue and 4 Green balls. One ball is drawn at random from each container. The probability that one of the balls is Red and the other is Blue will be
12/49
This problem involves calculating the probability of two independent events occurring: drawing a Red ball from the first container and drawing a Blue ball from the second container. Since the draws are independent, we can find the probability of each event separately and then multiply them to get the combined probability.
Ball Distribution in Containers
First, let's identify the number of balls of each color in both containers. This helps in understanding the total possibilities for drawing a ball from each container.
| Container | Red Balls | Green Balls | Blue Balls | Total Balls |
|---|---|---|---|---|
| Container 1 | 4 | 3 | 0 | 7 |
| Container 2 | 0 | 4 | 3 | 7 |
Probability of Drawing a Red Ball from Container 1
From the problem description, the first container holds 4 Red balls and 3 Green balls. To find the probability of drawing a Red ball, we use the formula:
$$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
For Container 1:
- Number of Red balls = 4
- Total balls = 4 (Red) + 3 (Green) = 7
So, the probability of drawing a Red ball from Container 1 is:
$$P(\text{Red from Container 1}) = \frac{4}{7}$$
Probability of Drawing a Blue Ball from Container 2
The second container contains 3 Blue balls and 4 Green balls. Similarly, to find the probability of drawing a Blue ball from this container:
- Number of Blue balls = 3
- Total balls = 3 (Blue) + 4 (Green) = 7
Therefore, the probability of drawing a Blue ball from Container 2 is:
$$P(\text{Blue from Container 2}) = \frac{3}{7}$$
Combined Probability of Red and Blue Balls
Since the event of drawing a ball from the first container is independent of drawing a ball from the second container, the probability that one ball is Red (from Container 1) AND the other is Blue (from Container 2) is the product of their individual probabilities:
$$P(\text{Red and Blue}) = P(\text{Red from Container 1}) \times P(\text{Blue from Container 2})$$
Substituting the probabilities we calculated:
$$P(\text{Red and Blue}) = \frac{4}{7} \times \frac{3}{7}$$
$$P(\text{Red and Blue}) = \frac{4 \times 3}{7 \times 7}$$
$$P(\text{Red and Blue}) = \frac{12}{49}$$
Therefore, the probability that one of the balls drawn is Red and the other is Blue is $\frac{12}{49}$.
Important Questions from Types of Probability
If f(x) is a probability density on the real line, then which of the following is NOT a valid probability density?
The probability of student A passing an exam is 2/7 and that of B passing is 5/7. If these probabilities are independent, what is the probability that only B passes the examination
A die is tossed three times, What is the probability of getting an odd number at least once ?
Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is
Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll of the dice and a ‘4’ on the second roll?
