To determine the probability that a 4 is drawn from Urn A followed by a 2 from Urn B, we'll break down the problem into two independent events and calculate their respective probabilities before combining them.
1. Probability of drawing a 4 from Urn A:
Urn A contains balls numbered from 1 to 8. Therefore, there are 8 balls in total. Since only one of these balls is numbered 4, the probability [tex]\( P(A) \)[/tex] of drawing a 4 from Urn A is:
[tex]\[
P(A) = \frac{1}{8}
\][/tex]
2. Probability of drawing a 2 from Urn B:
Urn B contains balls numbered from 1 to 3. Thus, there are 3 balls in total. Since only one of these balls is numbered 2, the probability [tex]\( P(B) \)[/tex] of drawing a 2 from Urn B is:
[tex]\[
P(B) = \frac{1}{3}
\][/tex]
3. Combined probability of the two events:
Since the events of drawing balls from Urn A and Urn B are independent, the combined probability [tex]\( P(A \text{ and } B) \)[/tex] of both events happening (drawing a 4 from Urn A followed by a 2 from Urn B) is obtained by multiplying the individual probabilities:
[tex]\[
P(A \text{ and } B) = P(A) \times P(B) = \frac{1}{8} \times \frac{1}{3} = \frac{1}{24}
\][/tex]
Therefore, the probability that a 4 is drawn from Urn A followed by a 2 from Urn B is [tex]\( \frac{1}{24} \)[/tex].
The correct answer is:
[tex]\[
\boxed{\frac{1}{24}}
\][/tex]
