SOLUTION: A received m good and n bad text messages, one of which was randomly deleted, and one good message was added before sending all to B. B also randomly deleted one message and added
Algebra.Com
Question 1200743: A received m good and n bad text messages, one of which was randomly deleted, and one good message was added before sending all to B. B also randomly deleted one message and added one good message before sending all to C. What is the probability that C will receive fewer bad messages than A? What is the probability that C will receive fewer bad messages than A, given that B randomly deleted and added one bad message? ([m, n] = [14, 6])
Answer by GingerAle(43) (Show Source): You can put this solution on YOUR website!
**1. Define Events and Probabilities**
* **A's Messages:**
* Good: m = 14
* Bad: n = 6
* Total: m + n = 20
* **A's Deletion:**
* Probability of deleting a good message: m / (m + n) = 14/20 = 7/10
* Probability of deleting a bad message: n / (m + n) = 6/20 = 3/10
* **B's Messages (after A's actions):**
* Good: m + 1 - (deleted by A)
* Bad: n - (deleted by A) + (added by A)
* **B's Deletion:**
* Probability of deleting a good message: (Good messages after A's actions) / (Total messages after A's actions)
* Probability of deleting a bad message: (Bad messages after A's actions) / (Total messages after A's actions)
* **C's Messages (after B's actions):**
* Good: (Good messages after B's actions) + 1
* Bad: (Bad messages after B's actions) - (deleted by B) + (added by B)
**2. Calculate Probabilities (General Case)**
* **Probability that C receives fewer bad messages than A:**
* This requires considering all possible scenarios of deletions and additions by A and B.
* This involves multiple conditional probabilities and can be quite complex.
**3. Calculate Probabilities (Given B deleted and added one bad message)**
* **B's Messages (given B deleted and added a bad message):**
* Good: m + 1 - (deleted by A)
* Bad: n - (deleted by A)
* **C's Messages (given B deleted and added a bad message):**
* Good: (Good messages after B's actions) + 1
* Bad: n - (deleted by A) - 1 + 1 = n - (deleted by A)
* **C receives fewer bad messages than A:**
* If A deleted a bad message:
* C's bad messages: n - 1
* C has fewer bad messages than A (which had n bad messages)
* If A deleted a good message:
* C's bad messages: n
* C has the same number of bad messages as A
* **Probability that C receives fewer bad messages than A given B deleted and added one bad message:**
* Probability that A deleted a bad message = 3/10
* Therefore, the probability is 3/10.
**For the specific case of [m, n] = [14, 6]:**
* **Probability that C receives fewer bad messages than A given B deleted and added one bad message is 3/10 or 0.3.**
**Note:**
* Calculating the probability for the general case without the specific condition on B's actions would involve a more extensive analysis of all possible scenarios.
I hope this explanation is helpful! Let me know if you have any further questions.
RELATED QUESTIONS
A received 6 good and 6 bad messages, accidentally deleted one, added one good and sent... (answered by CPhill)
Suppose 3 of the 12 bottles in a case of wine are bad. If you randomly select 2 bottles,... (answered by mathmate)
Person A has recieved 6 negative and 6 positive text messages. Person A randomly deletes... (answered by CPhill)
Nick traveled out of the country for a month. He purchased a plan from his cell phone... (answered by josmiceli)
Nick traveled out of the country for a month. He purchased a plan from his cell phone... (answered by Boreal)
Bob received five email messages yesterday in the following order: A, B, C, D, and E.... (answered by greenestamps)
Your cell phone company offers two text-messaging plans. One plan costs $.25 per text... (answered by MatrixWoman)
If you manufactured 67 parts and 4 parts were bad. What percentage was bad and what... (answered by Fombitz)
Your cell phone plan charges you $.02 to send a text message and $.07 to recieve a text... (answered by ankor@dixie-net.com)