Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
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]
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]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.