1. In a city, 20% of the citizens are carriers of a certain disease.If a citizen is a carrier, the probabbility that a blood test will indicate a positive result is 0.95. If citizen is a non-carrier, the probability that the blood test will indicate a postive result is 0.10. Two citizens are selected at random for the blood test. Find the probability that

(a) both citizens have positive results(b) both citizens have negative results

2. The probabilities that Alif, Kannan and Caili will pass an art examination are 4/5, 5/7, and 2/3 respectively. Find the probability that

(a) at least 1 of them will pass the art examination(b) Only Alif will pass the art examination

3. Suppose that 45% and 40% of Singaporeans approve and disapprove the idea of building a casino respectively. If three Singaporeans are interviewed at random,find the probability thata) all of them will either approve or disapprove of the idea

b) at least two of them will not approve of the idea

c) at most one of them will approve of the idea.

4. Given thatX = { x : x is an integer and 5 x 10 }Y = { y : y is a multiple of 3 and 1 y 10 }

An element is chosen at random from each set.Write down the total number of possible outcomes.

Using a probability diagram or otherwise, find the probability that:(i) the product xy is a perfect square.(ii) the product xy is an odd number.(iii) the product xy > 20.

5. Two bags each contains 91 balls. In each bag, there are 3 red balls, 1 white and the rest blue.

(i) One ball is drawn from the first bag. Find the probability that it is not blue.

(ii) One ball is drawn from the second bag. Find the probability that it is blue.

(iii) One ball is drawn from each bag. Find the probability that the two balls are(a) both blue,(b) each of a different colour.

6. Each member of a class of 30 boys supports one and only one of the three football teams; 13 boys support city, 10 support Rovers, and 7 support United.

(i) If a boy is to be chosen at random, what is the probability that he will support City?(ii) If 2 boys are to be chosen at random, what is the probability that they will both support City?

Find the probability that(iii) two boys chosen at random will support the same team.(iv) two boys chosen will support different teams.7. A certain brand of boxes of matches is advertised as having "average contents 50 matches". The probability that a box chosen at random will contain exactly 50 matches is 5/8.

(a) Calculate the probability that a box of matches chosen at random will not contain exactly 50 matches.

The probability that a box chosen at random will contain more than 50 matches is twice the probability that it will contain less than 50 matches.

(b) Calculate the probability that(i) one box chosen at random will contain at least 50 matches.(ii) of 2 boxes chosen at random, at least one will contain less than 50 matches.

8. Four bags, A, B, C and D each contains red discs and blue discs which are identical except for the colour.

Bag A contains 8 red discs and 2 blue discs.Bag B contains 6 red discs and 4 blue discs.Bag C contains 3 red discs and 5 blue discs.Bag D contains 1 red discs and 7 blue discs.

(i) A disc is taken at random from A. Find, as a fraction, the probability that the disc is blue.(ii) A disc is taken at random from B and another disc at random from C. Find, as a fraction, the probability that both discs are blue.(iii) Two discs are taken at random from D. Find the probability that at least one of the discs is blue.

9. (a) An ordinary six-sided die numbered 1 to 6 is thrown. Write down the probability that the number shown on the die is a prime number.

A six-sided die numbered 1 to 6 and an eight sided die numbered 3 to 10 are thrown together. Giving each answer as a fraction in its lowest terms, find the probability that(i) the sum of the numbers is 10,(ii) the two numbers are not equal.

(b) A pupil has difficulty in waking up for school, and so, to wake himself, he sets 3 alarms to go off at the same time, as the noise from at least 2 alarms is necessary to wake him. Each alarm goes off independently.The probability that each alarm goes off is 0.7, 0.8 and 0.9 respectively. Find the probability that(i) all 3 go off,(ii) the pupil is awakened.

10. Two dice are thrown. One is biased so that the probability of throwing a 6 is 1/16 and the probabilities of throwing the other five numbers are all equal. The other die is unbiased. Calculate, as a fraction in its lowest term, the probability that(i) both numbers thrown are not 6,(ii) at least one of the two numbers thrown is a 6,(iii) exactly one of the numbers thrown is a 4.

11. Nov 2002 P1 Q16(a) Two unbiased dice are thrown.Find the probability that they(i) show the same number(ii) show different number(b) Three unbiased dice are thrown.Find the probability that(i) they all show different numbers(ii) at least two show the same number12. Dunman High Prelims 2008 P1 Q9A small box containing chocolates of which 3 contains hazelnuts, 7 contains almonds and 2 contain sultanas. Two chocolates are picked at random, one at a time, without replacement. Find the probability that(a) both contain hazelnuts,(b) one contains almonds and one contains hazelnuts,(c) both are without sultanas.