To determine the probability of drawing a 4 from urn [tex]\(A\)[/tex] followed by a 2 from urn [tex]\(B\)[/tex], we need to follow these steps:
1. Find the probability of drawing a 4 from urn [tex]\(A\)[/tex]:
- Urn [tex]\(A\)[/tex] contains balls numbered 1 through 6. Therefore, there are 6 balls in total.
- Only one of these balls is numbered 4.
- Hence, the probability of drawing a 4 from urn [tex]\(A\)[/tex] is given by:
[tex]\[
\text{Probability of drawing a 4 from urn A} = \frac{1}{6}
\][/tex]
2. Find the probability of drawing a 2 from urn [tex]\(B\)[/tex]:
- Urn [tex]\(B\)[/tex] contains balls numbered 1 through 4. Thus, there are 4 balls in total.
- Only one of these balls is numbered 2.
- Thus, the probability of drawing a 2 from urn [tex]\(B\)[/tex] is:
[tex]\[
\text{Probability of drawing a 2 from urn B} = \frac{1}{4}
\][/tex]
3. Calculate the combined probability of both events occurring:
- Since drawing a 4 from urn [tex]\(A\)[/tex] and drawing a 2 from urn [tex]\(B\)[/tex] are independent events, we multiply the probabilities of each event.
- Therefore, the combined probability is:
[tex]\[
\text{Combined probability} = \left(\frac{1}{6}\right) \times \left(\frac{1}{4}\right) = \frac{1}{24}
\][/tex]
Thus, the probability that a 4 is drawn from urn [tex]\(A\)[/tex] followed by a 2 from urn [tex]\(B\)[/tex] is [tex]\(\frac{1}{24}\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{\frac{1}{24}}
\][/tex]
