Tutorial Questions

(Discrete and Continuous Probability Distributions)

1. When the secretary at IFM is in a hurry to go home, the probability that a mistake will be made in addressing a letter is 0.25. If the secretary has to send to the post office 6 letters just before closing time, find the probability that the secretary will make a mistake in addressing at least two of these letters

2. If 20% of dume produced by dume factory are defective, determine the probability that 4 dumes bought the one who cares at random one will be defective and for sure will not help in control of this deadly infection of nowadays.

3. In Nanyamba village in Mtwara Rural District, the average korosho farm size is 150 Acres with a variance of 2,500 acres. If one farm is selected at random from that gifted village, determine the probability that it has between 200 and 300 acres assume normality in Nanyamba.

4. A bag contains one red and seven white marbles. A marble is drawn from the bag and its colour is observed. Then the marble is put back into the bag and the contents are thoroughly mixed. Using the Poisson approximation to the binomial distribution, find the probability that in 8 such drawings a red ball is selected exactly three times.

5. A box contains five red, four white and three blue balls. A ball is selected at random from the box, its colour is noted, and then the ball is replaced. Find the probability that out of 6 balls selected in this manner three are red, two are white, and one is blue.