Question

Urn A has balls numbered 1 through 7. Urn B has balls numbered 1 through 3. What is the probability that a 4 is drawn from A followed by a 2 from​ B?
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Part 1
A.one seventh
one seventh
B.StartFraction 2 Over 21 EndFraction
StartFraction 2 Over 21 EndFraction
C.StartFraction 1 Over 21 EndFraction
StartFraction 1 Over 21 EndFraction
D.StartFraction 10 Over 21 EndFraction
StartFraction 10 Over 21 EndFraction

Answer 1

To find the probability of drawing a 4 from Urn A followed by a 2 from Urn B, we will calculate the individual probabilities for each step and then multiply them together, as these events are independent.

1. **Probability of drawing a 4 from Urn A:**
- Urn A has balls numbered from 1 to 7, which means there are 7 possible outcomes.
- There is only 1 ball with the number 4.
- Therefore, the probability of drawing a 4 from Urn A is:
\[
P(4 \text{ from A}) = \frac{1}{7}
\]

2. **Probability of drawing a 2 from Urn B:**
- Urn B has balls numbered from 1 to 3, which means there are 3 possible outcomes.
- There is only 1 ball with the number 2.
- Therefore, the probability of drawing a 2 from Urn B is:
\[
P(2 \text{ from B}) = \frac{1}{3}
\]

3. **Combined probability:**
Since the events are independent, we multiply the probabilities:
\[
P(4 \text{ from A and then } 2 \text{ from B}) = P(4 \text{ from A}) \times P(2 \text{ from B}) = \frac{1}{7} \times \frac{1}{3} = \frac{1}{21}
\]

Thus, the probability that a 4 is drawn from A followed by a 2 from B is:
\[
\frac{1}{21}
\]

Therefore, the answer is:

**C.** StartFraction 1 Over 21 EndFraction