Conditional Probability

Probability (प्रायिकता)|Set Theory (समुच्चय सिद्धांत)|Permutation And Combination In Probability (क्रमचय तथा संचय प्रायिकता में)|Conditional Probability (सशर्त संभाव्यता)|Independent Event (स्वतंत्र घटनाएं)|Questions (प्रश्न)|OMR

Consider the following statements related to the nature of Bayes' theorem 1. Bayes' theorem is a formula for computation of a conditional probability. 2. Bayes' theorem modifies an assumed probability of an event in the light of a related event which is observed. Which of the statements given above is/are correct ?

7. Ancing 6-year-old college professors, 90% are nonsmokers and 10% are smokers. The probabil- ity of a nonsmoker dying in the next year is 0005 and the probability for smokers is 0.05. Given that one of this group of college professors dies in the next ye r, what is the conditional probability that the professor was a smoker?

A biased coin is tossed repeatedly until a tail appears for the first time. Heads is 3 times as likely to appear as tails. Let x be the number of tosses required. Assume that all the trials of tossing a biased coin are independent. Then, the conditional probability that xge6 , gives that x gt3 , is equal to

In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03 The conditional probability that an error is committed in processing given that Sonia processed the form is :