Melody

Hi Terence :)

(a) superior construction Pte Ltd is a successful company dealing with many major projects in singapore.

recently, it has summited its biddings for two major govt projects. projects A worth $120million and the company believes it has 40% chance of securing the projects. project B worth $1.8 billion and there is 30% chance the company can win the project.both project are independent of each other. what is the probability that the company:

The value of the projects is irrelevant to this question.

It is best to draw a venn diagram to answer questions like these. In this case that will be two overlaping circles representing success in secruing A and B projects and a surounding rectangle whit the probability of not getting either project. This will help you work out what you are bing asked for. I can draw it if you need me to but its a hassle and you can probably do it for yourself on a peice of paper.

We have

P( securing A) = 0.4

P( securing B) = 0.3

P(securing both)=0.3*0.4=0.12

P(securing A but not B) = 0.4-0.12 = 0.28

P(securing B but not A)= 0.3-0.12 = 0.18

P(securing either) = 0.4+0.3-0.12 = 0.58       This includes the prob of securing both

P(securing neither) = 1-P(securing either) = 1- 0.58 = 0.42

(i) will secure Project A or B but not both = 0.28+0.18 = 0.46

(ii) will not secure project A or will not secure project B =  1 - P(securing both) = 1-0.12 = 0.88

(b) do you agree that "if two events are mutually exclusive then these two events will be independent"?  Why?

NO If they are mutually exclusingve then the outcome of one impacts the outome of the other.

If the two events above were mutually exclusive that would mean that if the bid for A was successful then the bid for B must be unsucessful and vise versa. So the 2 circles in the ven diagram would not overlap.

(c) provide one business-related example each, with explanation, for mutually exclusive and independent events 

the first two is the most important(I-II)

a reward shall be given

10^2.15

10^2.15 = 141.2537544622754302      (This is approximate)

There is no x^2 terms so the coeffcient of x^2 is 0

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(a) The candies are all different and the lunch boxes are all different?
Say the lunch boxes are red, blue and yellow and the  candies are X,Y,Z

(b) The candies are all the same and the lunch boxes are all the same?
3 in 1 and none in the others

2 in one box and 1 in another

1 in each box

6 ways

(c) The candies are all the same and the lunch boxes are all different?

(d) The candies are all different and the lunch boxes are all the same?

(e) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different?

That is what I get :/   My answers should be checked though :)

Thank you Heureka,

Now I am very happy :))

I do not understand what you mean Max :/

Here is a pretty tesselation, what angles are you referring to?

Of course Max is correct, there has to be an angle there. :)

or

(tan30)^2 = 1/3

The calc changes it to tan30^2 but that is ok :)

(tan(30))^2 = 0.3333333333337655

It should just be 1/3 so there is some rounding error.

I don't have a general answer for you, but that is a good question ://

\(\int_{0}^{5} h(x)dx = 0\)

That is what I got after trying to figure out the area of a square using an integral. h(x) = 5 creating a square... the area is 25 but why this integral no work? A line is a curve too!!!

h(x)=5

\(A=\int_{0}^{5} h(x)dx \\ =\int_{0}^{5} \;5\:dx \\ =\left[5x\right]_0^5\\ =25-0\\ =25 units^2 \)

My integral works just fine.