1.A salesman has the following record of sales during three weeks for the three items X, Y and Z which have different rates of commission.

Week

Unit Sold

Total Commission Required (in Rs.)

X

Y

Z

X

40

30

20

270

Y

50

50

40

450

Z

60

30

10

260

Find out, using Cramer's method, rates of commission on items X, Y and Z10 Marks

2.In a recent survey of 300 people regarding TV programs, 160 watched KTN, 150 watched NTV and 150 watched Kiss TV. 90 people watched both KTN and NTV,70 people watched NTV and Kiss TV, 100 people watched KTN and Kiss TV. If 40 people watched all the three networks10 Marks

i.How many did not watch any of the three networks

ii.How many watched two channels only

iii.How many watched one channel only

iv.How many did not watch Kiss TV

v.How many did not watch KTN or NTV

3.The probability that machine A will be performing a useful function in five years time is 0.25, while the probability that machine B will still be operating at the end of the same period is 0.33. find the probability that, in five years time15 Marks

i.Both machines will be performing a useful function

ii.Neither will be operating

iii.Only machine B will be operating

iv.At least one of the machines will be operating

v.Only machine A will be operating

4.Three machines, A, B and C produce respectively 60%, 30% and 10% of the total production of a factory. The percentages of defective production for each machine are 2%, 4% and 6% respectively.10 Marks

i.If an item is selected at random, find the probability that the item is defective

ii.If an item is selected at random and found to be defective, what is the probability that the item was produced by machine A