1) A social worker has studied the rate of illiterate problem among 300 PLKN trainees in a certain PLKN campsite and her findings are summarized in the following table.

Illiterate Literate

Male 60 120

Female 30 90

a) If a trainee is selected at random, what is the probability that the trainee is a male and illiterate?

b) Given that a trainee selected at random is literate, what is the probability that the trainee is a female?

c) Calculate the probability that a trainee selected at random is a male or illiterate.

2) The probability that a patient is allergic to penicillin is 0.2. Suppose that this drug is administered to three patients. Find

a) The probability that all the three patients are allergic to the penicillin.

b) The probability that at least one of them is not allergic to the penicillin.

3) In a group of 2500 persons, 1400 are female, 600 are vegetarian and 400 are female and vegetarian. What is the probability that a randomly selected person from this group is:

a) A male and vegetarian.

b) A female or non- vegetarian.

c) A male given that he is vegetarian.

3) A batch of 200 boxes of frozen orange juice contains 5 boxes that are defective. Two boxes are selected at random without replacement.

i) Draw a tree diagram for the above experiment.

ii) Find the probability that the second box is defective given that the first box is defective.

iii) Find the probability that both boxes are defective.

iv) Find the probability that both boxes are non-defective.

4) Three students are taking part in a Statistics Contest. The probabilities that they become the champion are 0.25, 0.37 and 0.28 respectively. Assuming that the probability that a student becomes a champion is independent of each other. What is the probability that:

a) One of them becomes the champion?

b ) None of them becomes the champion?

5) Use the letters in the word " IMELDA " and tell how many 6-letter arrangements, with no repetitions, are possible if the :

a) First letter is a vowel.

b) Vowels and consonants alternate, beginning with a consonant.