MATHEMATICS

Question

1) The probability. Of three events A,B,C, happening are 1\2, 2\3, 1\4.find the probability that events A and C only occur 2) Find the sum of 70,69,68,...........21. 3) James and daniel owners of J.Dm chemicals shared theiir end of the year profit in the ratio of 4:6 if daniel (D) got N4,000 more thann james (J), calculate their total annual Profit 4) What is the probability thhat 3customers waiting in a bank will be served in the sequence of their arrival at the bank 5) On four successive days,a farmer picks exxactly twice as many apples each day as on the previous day. If in the course course of the four days he picks a total of 12,000 apples how many apples does he pick on the third of the four days?

Answer 1

1. Assuming the events are independent, the probability of B not happening is 1-⅔=⅓, so the probability of A and C but not B=½×¼×⅓=1/24.
2. 70+69+...+22+21 can be written (70+21)+(69+22)+(68+23)+...+(46+45)=91×25=2275.
3. J/D=4/6=2/3; D=J+4000. J=2D/3, D=2D/3+4000, 3D=2D+12000, D=12000, J=8000. D+J=20000, total profit.
4. There are 6 ways they can arrive: ABC, ACB, BAC, BCA, CAB, CBA, therefore there is a probability of ⅙ that they will be served in the order they arrive, assuming there are no other factors.
5. First day he picks a apples, 2nd day: 2a, 3rd day: 4a, 4th day: 8a, total 15a apples=12000, a=800. On the third day he picks 4a=3200 apples.