1. Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier?
1. Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the
2. Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if
a. A answers the first question,
b. B answers the first question.
3. Patients are recruited onto the two arms (0 - Control,1-Treatment) of a clinical trial. The probability that an adverse outcome occurs on the control arm isp0, and isp1for the treatment arm. Patients are allocated alternately onto the two arms, and their outcomes are independent. What is the probability that the first adverse
4. In a tennis match, with the score at deuce, the game is won by the first player who gets a clear lead of two points. If the probability that given player wins a particular point is θ, and all points are played independently, what is the probability that player eventually wins the game?
5. While watching a game of Champions League football in a cafe, you observe someone who is clearly supporting Manchester United in the game. What is the probability that they were born within 25 miles of Manchester?
Assume that:
- the probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is 1/20 ;
- the chance that a person born within 25 miles of Manchester actually supports United is 7/10;
- the probability that a person not born within 25 miles of Manchester supports United with probability1/10
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