To determine the probability that a 4 is drawn from Urn A followed by a 2 from Urn B, we need to calculate the probabilities of these individual events and then find their product since these events are independent.
1. Calculate the probability of drawing a 4 from Urn A:
- Urn A contains balls numbered from 1 to 6.
- Thus, there are a total of 6 balls in Urn A.
- There is only 1 ball numbered 4 in Urn A.
- The probability of drawing the ball numbered 4 from Urn A is:
[tex]\[
\text{Probability of drawing a 4 from Urn A} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{6}
\][/tex]
2. Calculate the probability of drawing a 2 from Urn B:
- Urn B contains balls numbered from 1 to 4.
- Thus, there are a total of 4 balls in Urn B.
- There is only 1 ball numbered 2 in Urn B.
- The probability of drawing the ball numbered 2 from Urn B is:
[tex]\[
\text{Probability of drawing a 2 from Urn B} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{4}
\][/tex]
3. Calculate the combined probability of drawing a 4 from Urn A followed by a 2 from Urn B:
- Since the draws from Urn A and Urn B are independent events, the total probability is the product of the individual probabilities:
[tex]\[
\text{Total probability} = \left(\frac{1}{6}\right) \times \left(\frac{1}{4}\right) = \frac{1}{6} \times \frac{1}{4} = \frac{1}{24}
\][/tex]
Therefore, the probability that a 4 is drawn from Urn A followed by a 2 from Urn B is:
[tex]\[ \boxed{\frac{1}{24}} \][/tex]
