Assist me in solving the attached questions. Pls, I was not able to open the previous questions answer sent to me.
18 A Three machines, X, Y and Z are used to produce greeting cards.
During a days production, X produces 4880 cards, Y produces 3728 cards and Z does 3152 cards. The probability of X producing a defective card is 0.1, that of Y is 0.3 and that of Z is 0.1. Find the probability that at the end of the day, one card selected at random will be defective.
B It is estimated that there is a 15% chance that unemployment will increase by more than 3% next year. If this increase does occur, then there will be 95% chance that congress will enact a federally funded job programme. Otherwise, the probability of such a programme being funded is 10%. Suppose that the job programme was funded by congress;
(a) what is the probability that unemployment grows by more than 3%? (b) what is the probability that unemployment did not rise by more than 3%?
19 I In how many ways can a number be chosen from 51 - 75 such that
Alt is a multiple of 6 or 9?
B It is a multiple of 3 or 4?
II One has 15 pairs of trousers and 23 shirts, in how many ways could the person combine these clothes if he wears a pair of jeans and a shirt at a time?
III In how many ways could a supermarket manager display 13 brands of cereals in 7 spaces on a shelf?
IV How many different number plates for cars could be made if each number plate contains four (4 of the digits from 0 9 followed by a letter A Z (not including O), and prefixed with GW, assuming that
a no repetition is allowed
b) repetition is allowed
V In how many ways can the letters of the word STATISTICS and that of MATHEMATICS be arranged?
20 I How many combinations are there if 22 distinct things are considered taking 9 at a time?
II In how many different ways can 11 of 35 lecturers be selected to assist with the preparation of exams?
III A statistics lecturer sets 7 questions in an end of semester exam and students were asked to attempt any 4 of them. Find the number of ways of selecting these questions.
IV In how many ways could a committee comprising of 9 men and 6 women be formed from a group of 18 men and 7 women?
V A box contains 22 red, 25 white and 18 blue balls. If 6 balls one drawn at random simultaneously, find the probability that
A all are red
B4 are red and 2 white
C at least one is red
D 2 of each colour is drawn
21 I In a group of 11 boys and 9 girls, 5 are to be selected. In how many ways can they be selected such that at least one boy should be there
II There are 9 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
22 The data below is a distribution of the marks (with a maximum of 45 obtained by students in a test. Investigate whether the data is negatively or positively skewed.
Marks 31-35 Frequency27
36-40 20
41-45 23
46-50 21
51-55 18
56-60 33
61-65 20
