1.
The number of cars sold per week in a particular showroom has a Poisson i) ii) distribution with mean 6. Calculate the probability that in a week exactly 8 cars are sold. at least 3 cars are sold iii) between 5 and 7 (inclusively) cars are sold.
2.
On a production line, on average there are 2 faulty products per 100 items a) Calculate the exact probability that in a batch of 50 items i) there are no faulty products ii) there are at least 2 faulty products b) Using the appropriate approximation, estimate these two probabilities.
3.
A coin is tossed until the first head appears. Calculate the probability that i) ii) the coin is tossed exactly once the coin is tossed exactly three times iii) the coin is tossed at least three times iv) the number of tosses is odd.
4.
In a lottery 5 numbers are chosen without replacement from 30. Calculate the probability of i) winning the jackpot (choosing all 5 numbers correctly) ii) winning the smallest prize (choosing 3 of the 5 numbers correctly) iii) choosing at least one of the numbers correctly.
5.
A die is rolled n times. Let S be the sum of the results. Calculate E(S) and
Var(S).