VCE Methods Question Thread!

[barydos]

More probability questions coming your way!




I'm particularly curious how to find out part b) and c) :S

[Jenny_2108]

^ Tbh, I'm really bad at probability. I'll try it, if I do wrong, correct me

b) First, you have to find probability distribution
Dunno how to draw the table in LaTex though

There are 2 situtations: satify (S) and not satisfy (S')
Its better to draw tree diagram so you can see that
If its S, the prototypes will go into production. if its S', there are 2 types of probabilities next time: S and S'

Pr(S at first time)=0.65 => cost 7 millions
Pr(S second time)=0.35 x 0.65= 0.2275 => cost 7+3.5 (half of 7)=10.3 millions
Pr(S at third time or abandoned)=0.35 x 0.35 x 0.35 + 0.35 x 0.35 x 0.65=0.1225 => cost 7+3.5+1.75=12.25 millions

So E(X)= 7 x 0.65+10.3 x 0.2275 + 12.25 x 0.1225 = 8.393875

c) If the machine developed, income will be 20 millions

Total income=(0.65+0.2275+0.35x0.35x0.65) x 20=19.1425 millions

Profit = income - cost = 19.1425 - 8.393875 = 10.748 millions

[barydos]

^ Tbh, I'm really bad at probability. I'll try it, if I do wrong, correct me

b) First, you have to find probability distribution
Dunno how to draw the table in LaTex though

There are 2 situtations: satify (S) and not satisfy (S')
Its better to draw tree diagram so you can see that
If its S, the prototypes will go into production. if its S', there are 2 types of probabilities next time: S and S'

Pr(S at first time)=0.65 => cost 7 millions
Pr(S second time)=0.35 x 0.65= 0.2275 => cost 7+3.5 (half of 7)=10.3 millions
Pr(S at third time or abandoned)=0.35 x 0.35 x 0.35 + 0.35 x 0.35 x 0.65=0.1225 => cost 7+3.5+1.75=12.25 millions

So E(X)= 7 x 0.65+10.3 x 0.2275 + 12.25 x 0.1225 = 8.393875

c) If the machine developed, income will be 20 millions

Total income=(0.65+0.2275+0.35x0.35x0.65) x 20=19.1425 millions

Profit = income - cost = 19.1425 - 8.393875 = 10.748 millions

I refuse to believe you are bad at probability!
This is all correct, thank you so much, you're AMAZING!

[barydos]

I'm under the impression that you do not need to do the other parts to complete part 3b), but I put the rest of the questions up here just in case.
So yeah, I'm after question 3. b), I can't seem to get it. :S

[dinosaur93]

But in after 4 years...



YES, because Dr Arnold will go out of business in 4 years time...


btw, How did you solve 3a??

[barydos]

But in after 4 years...



YES, because Dr Arnold will go out of business in 4 years time...


btw, How did you solve 3a??

so is it just trial and error with calculator? is there any other trick to solve it?

and for part 3a):
Using that a/(a+b) formula for steady state.... aka

(1-b)/(1-b+0.2) * 10 000 >= 4000
solve for b to be b>=0.7

then use the other one
0.2/(1-b+0.2)*10 000 >=4000
solve for b to be b=<0.867

combine the two
you get 0.7=<X=<0.867

[dinosaur93]

Is this right by any chance?

Circular Function

   

basic angle =

[dinosaur93]

But in after 4 years...



YES, because Dr Arnold will go out of business in 4 years time...


btw, How did you solve 3a??

and for part 3a):
Using that a/(a+b) formula for steady state.... aka

(1-b)/(1-b+0.2) * 10 000 >= 4000
solve for b to be b>=0.7

then use the other one
0.2/(1-b+0.2)*10 000 >=4000
solve for b to be b=<0.867

combine the two
you get 0.7=<X=<0.867

tnx..

so is it just trial and error with calculator? is there any other trick to solve it?

The question specifically asked at which year and who , so I guess its a matter of trial error

[barydos]

Is this right by any chance?

Circular Function

   

basic angle =

Firstly, you should look back your domain to double check your answers. In this case, you went wrong somewhere.

Here's my method.
Since it's modulus'd, I solved
sin(x-pi/6) = sqrt(3)/2 and sin(x-pi/6) = - sqrt(3)/2
so i get
x-pi/6 = pi/3, 2pi/3  and 4pi/3, 5pi/3 for the negative one
after adding the pi/6 over
you should get

pi/2, 5pi/6, 3pi/2 and 11pi/6 which is your answer

(sorry for not using LaTeX, haven't learnt it yet LOL)

[dinosaur93]

Is this right by any chance?

Circular Function

   

basic angle =

Firstly, you should look back your domain to double check your answers. In this case, you went wrong somewhere.

Here's my method.
Since it's modulus'd, I solved
sin(x-pi/6) = sqrt(3)/2 and sin(x-pi/6) = - sqrt(3)/2
so i get
x-pi/6 = pi/3, 2pi/3  and 4pi/3, 5pi/3 for the negative one
after adding the pi/6 over
you should get

pi/2, 5pi/6, 3pi/2 and 11pi/6 which is your answer

(sorry for not using LaTeX, haven't learnt it yet LOL)

oh, now I see where I went wrong...

tnx..

[barydos]

Ugghhh more probability questions coming up!
sorry everyone haha

[dlqudcjf]

This is an inverse standard normal distribution question. (probability)
Using Z~N(0,1), find k such that:
Pr(|Z|<k) = 0.85
Someone help me please.

[BubbleWrapMan]

This is an inverse standard normal distribution question. (probability)
Using Z~N(0,1), find k such that:
Pr(|Z|<k) = 0.85
Someone help me please.

(using symmetry and complements)

[Jenny_2108]

Ugghhh more probability questions coming up!
sorry everyone haha

(Image removed from quote.)

Firstly, you calculate probability of non-defective items
For example:
Pr(defective)=0.01 => Pr(non-defective)=1-0.01=0.99
There are 10 items => 0.99^10=0.90438

Similar to others as well, then put in CAS to plot the graph

[Bhootnike]

Find the probability of getting at least nine successes in 100 trials for which the probability of success is p = 0.1.

2 questions:

1.is this a calc question?
2. how do you do it lol