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(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:

(i) will secure Project A or B but not both

(ii) will not secure project A or will not secure project B

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

(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

terenceHiroyuki  Jun 29, 2017
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#1
+89837
+1

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

Melody  Jun 29, 2017
#2
+89837
+1

Terence has asked me for more explanation so I shall explain some more:

(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    given

P( securing B) = 0.3     given

P(securing both)=0.3*0.4=0.12    If you wnat the probablility of 2 independent events happening then you muliply the probabilities together.

Underneath in the box is supposed to be 'neither A NOR B'   This is what is outside the circles.

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

You can see from the diagram that the 0.12 is included in both circles.

If you do not subtract it here then you will have added it in TWICE. You don't want that :)

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

I've subtracted the prob of getting any contract from 1 because the possibility of anything at all happening is 1.

(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

Does that help?

Melody  Jul 1, 2017
edited by Melody  Jul 1, 2017
edited by Melody  Jul 1, 2017

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