Basic Statistics05 marksNumerical: Bayes theorem probabilityConditional probability and Bayes theorem
Suppose Rajesh receives 50 messages and Harish receives 90 messages in the personal emails respectively. Please note that the email address of Rajesh and Harish is different. Rajesh receives 1% junk emails, and Harish receives 2% junk emails. A person is chosen at random at the end of a day and foun
Suppose Rajesh receives 50 messages and Harish receives 90 messages in the personal emails respectively. Please note that the email address of Rajesh and Harish is different. Rajesh receives 1% junk emails, and Harish receives 2% junk emails. A person is chosen at random at the end of a day and found the email message is junk. What is the probability that this junk email found in the Harish's email inbox? [5]
- Rajesh messages: 50, junk rate = 1% = 0.01 - Harish messages: 90, junk rate = 2% = 0.02 - Total messages: 50 + 90 = 140 - Find: $P(\text{Harish} \mid \text{Junk})$ Define events: - $R$ = email from Rajesh, $H$ = email from Harish, $J$ = email is junk Prior probabilities: $$P(R) = \frac{50}{140}...