Question 1193749: A sample space has three possible outcomes, B, C, and D. It is known that P(C) = P(D). The operation of the chance mechanism is simulated 10,000 times (runs). The sorted frequencies of the three outcomes (B, C, and D) are: 2322, 2360, and 5318.
(a) What is your approximation of P(B)? To receive credit you must explain your answer.
(b) What is the best approximation of P(C)? To receive credit you must explain your answer.
Answer by proyaop(69)   (Show Source):
You can put this solution on YOUR website! ### (a) Approximation of \( P(B) \)
To approximate \( P(B) \), divide the observed frequency of \( B \) by the total number of runs.
\[
P(B) = \frac{\text{Frequency of } B}{\text{Total Runs}}
\]
Where:
- Frequency of \( B = 2322 \),
- Total runs = \( 2322 + 2360 + 5318 = 10000 \).
Substitute values:
\[
P(B) = \frac{2322}{10000} = 0.2322
\]
### (b) Best Approximation of \( P(C) \)
It is given that \( P(C) = P(D) \). Since the frequencies of \( C \) and \( D \) are 2360 and 5318 respectively, the best way to approximate \( P(C) \) and \( P(D) \) is to split the combined probability equally between them.
#### Step 1: Find \( P(C) + P(D) \)
The combined probability of \( C \) and \( D \) is:
\[
P(C) + P(D) = \frac{\text{Frequency of } C + \text{Frequency of } D}{\text{Total Runs}}
\]
Substitute values:
\[
P(C) + P(D) = \frac{2360 + 5318}{10000} = \frac{7678}{10000} = 0.7678
\]
#### Step 2: Split Equally Between \( P(C) \) and \( P(D) \)
Since \( P(C) = P(D) \):
\[
P(C) = P(D) = \frac{P(C) + P(D)}{2} = \frac{0.7678}{2} = 0.3839
\]
### Final Answers:
(a) \( P(B) = 0.2322 \)
(b) \( P(C) = 0.3839 \)
|
|
|
