MAT 271 -PRACTICE EXERCISE li 1. A landscaper has 4 mangos, 3 oranges and 2 grape trees to be planted in a row. How many different arrangements can be made? 2. In how many ways can a committee of 7 members be selected from 10 boys and 12 girls such that (i). There are at least 4 girls. (ii). There are at most 2 boys. (ii) The committee has at least 2 girls and not less than 3 boys. 3. A card is picked at random from a ordinary deck of 52 cards. Find the probability that the card is either club or ace. 4. If two fair dice are tossed, what is the probability that their sum is less than or equal to 5, given that at least one face shows a 2? 5. Let A and B be two events associated with an experiment, and suppose P(A)=0.5 and P(AUB)=0.8. Let P(B) = p. For which values of pare: (a) A and B independent? (b) A and B mutually exclusive? 6. A card is drawn from a standard deck of 52 cards and then a second is drawn without replacing the first card. If we know that the second card is a spade, what is the probability that the first card is a spade? 7. There are two identical boxes A and B. Box A contains 4 red plugs and 3 blue plugs. Box B contains 5 red plugs and 1 blue plug. The experiment is to choose a box at random and from this select two plugs one after another without replacing the plug that was selected first, then select a second plug. (i) What is the probability of selecting plugs of the same colour? (ii) What is the probability that the second plug selected is red? (iii) What is the probability that at least one plug is blue? 8. Let A and B be events with P(A) = 0.75, P (B) = 0.6 and P(AB)=0.15 Compute: (a) P (AB) (b) P (BA) (c) P(A|B) (d) P (B | A) (e) Are A and B independent? Explain why? (f) Are A and B mutually exclusive events? Explain Why? 9. One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white balls and 5 black balls. One ball is drawn from the first bag and placed unseen in the second bag. (a) Display the probability tree for the experiment. (b) What is the probability that a ball drawn from the second bag is black? 10. If P(A)=0.3, P(B | A) = 0.7, P(B | A)=0.2, P(C | AN B)-0.2, P(C| A B)=0.15 P(CAB)=0.8 and P(C | AB²)=0.9