Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine the conditional probability [tex]\(P(A \mid B)\)[/tex], which is the probability that a randomly selected student is in the chess club given that they are in the karate club, we can use the formula for conditional probability:
[tex]\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \][/tex]
Here, [tex]\(P(A \cap B)\)[/tex] is the probability that a student is in both the chess club and the karate club, and [tex]\(P(B)\)[/tex] is the probability that a student is in the karate club.
Based on the information provided:
- There are 10 students in total.
- 4 students are in the chess club.
- 3 students are in the karate club.
- 2 students are in both clubs.
First, we need to calculate [tex]\(P(A \cap B)\)[/tex]:
[tex]\[ P(A \cap B) = \frac{\text{Number of students in both clubs}}{\text{Total number of students}} = \frac{2}{10} = 0.2 \][/tex]
Next, we calculate [tex]\(P(B)\)[/tex]:
[tex]\[ P(B) = \frac{\text{Number of students in the karate club}}{\text{Total number of students}} = \frac{3}{10} = 0.3 \][/tex]
Now, we can calculate [tex]\(P(A \mid B)\)[/tex]:
[tex]\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{0.2}{0.3} \][/tex]
[tex]\[ P(A \mid B) = \frac{2}{3} \][/tex]
Converting [tex]\(\frac{2}{3}\)[/tex] to a decimal:
[tex]\[ \frac{2}{3} \approx 0.6667 \][/tex]
Thus, the conditional probability [tex]\(P(A \mid B)\)[/tex] is approximately [tex]\(0.6667\)[/tex]. The given answer of [tex]\(\frac{2}{10} = 0.20\)[/tex] is incorrect.
[tex]\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \][/tex]
Here, [tex]\(P(A \cap B)\)[/tex] is the probability that a student is in both the chess club and the karate club, and [tex]\(P(B)\)[/tex] is the probability that a student is in the karate club.
Based on the information provided:
- There are 10 students in total.
- 4 students are in the chess club.
- 3 students are in the karate club.
- 2 students are in both clubs.
First, we need to calculate [tex]\(P(A \cap B)\)[/tex]:
[tex]\[ P(A \cap B) = \frac{\text{Number of students in both clubs}}{\text{Total number of students}} = \frac{2}{10} = 0.2 \][/tex]
Next, we calculate [tex]\(P(B)\)[/tex]:
[tex]\[ P(B) = \frac{\text{Number of students in the karate club}}{\text{Total number of students}} = \frac{3}{10} = 0.3 \][/tex]
Now, we can calculate [tex]\(P(A \mid B)\)[/tex]:
[tex]\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{0.2}{0.3} \][/tex]
[tex]\[ P(A \mid B) = \frac{2}{3} \][/tex]
Converting [tex]\(\frac{2}{3}\)[/tex] to a decimal:
[tex]\[ \frac{2}{3} \approx 0.6667 \][/tex]
Thus, the conditional probability [tex]\(P(A \mid B)\)[/tex] is approximately [tex]\(0.6667\)[/tex]. The given answer of [tex]\(\frac{2}{10} = 0.20\)[/tex] is incorrect.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.