Box A contains 4 defective and 6 non-defective items. Box B contains 3 defective and 7 non-defective items. A box is picked at random and then an item is drawn from it.

Find the probability:

i) Draw a tree diagram to represent the information.
ii) Of drawing a defective item.
iii) Of drawing a non-defective item.
iv) That box A was picked given that a defective item has been drawn.
v) That box B was picked given that a non-defective item was drawn.

A manufacturer makes ball pens. The manufacturer employs an inspector to check the quality of his product. The inspector tested a random sample of the pens from a large batch and calculated the probability of any pen being defective as 0.25.Peter buys two of the pens made by the manufacturer.

i) Draw a tree diagram to illustrate the information
ii) Calculate the probability that both pens are defective.
iii) Calculate the probability that exactly one of the pens is defective.

A group of 50 students was asked which of three daily newspapers they read, Nation Standard and Star. The results showed that 25 read Nation, 16 read Standard and 14 read Star, 5 read both Nation and Standard, 4 read Standard and Star while 6 read Nation and Star and 2 read all the three.

i) Illustrate these data on Venn diagram.

ii) Find the probability that a person selected at random from this group reads;

i) At least 1 of the newspapers.

ii) None of the newspapers.

iii) Only 1 of the newspapers.

iv) Only the Nation.