My thread of questions

[shinny]

I don't understand. I thought if E cannot occur then N would be 1-0.5

How so? The only events available that can happen is E or N. If E cannot occur twice consecutively, and E has already occurred on the first trial, then on the second trial, E cannot occur. If E cannot occur, then the only option left is for N to occur on the second trial, making the probability of N occurring 100%. Can you explain to me how you got 1-0.5 and maybe I could figure out what you don't understand?

[cobby]

At each of a series of trials, the probability of the occurence of a certain event is 0.5, except this cannot occur in 2 consecutive trials.

Show that the prob. of it occuring just twice in three trials is 0.25.
ans.
E=event
N=no event

ENE= 0.5*1*0.5= 0.25

My Question: why is N, 1?

I did it this way..

First draw a tree diagram of all the possible events, then rule out all the options that have two consecutive occurrences left

Which should be ENE and NEN

Therefore the probabilities are

(0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) = 0.25

[khalil]

I don't understand. I thought if E cannot occur then N would be 1-0.5

How so? The only events available that can happen is E or N. If E cannot occur twice consecutively, and E has already occurred on the first trial, then on the second trial, E cannot occur. If E cannot occur, then the only option left is for N to occur on the second trial, making the probability of N occurring 100%. Can you explain to me how you got 1-0.5 and maybe I could figure out what you don't understand?

Yep i understand know shinny, thanks

[khalil]

Katia and Mikki play a game in which a fair six-sided die is thrown 5 times. Katia will recieve $1 from Mikki if there is an odd number sixes, and Mikki will recieve $x from Katia if there is an even number of sixes. Find x for the game to be fair. (count zero as even)

ans. 76 cents

[Flaming_Arrow]

first you have to assign which is player is positive, ill take katia as positive
so its 1 and -x

1 = Pr(1) + Pr(3) + Pr(5)
-x = Pr(0) + Pr(2) + Pr(4) or you can just do 1-(Pr(1) + Pr(3) + Pr(5))

now in order it to be fare mean must equal zero

so Pr(1) + Pr(3) + Pr(5) - x(Pr(0) + Pr(2) + Pr(4)) = 0

solve for x

[khalil]

ok thanks...
A newspaper seller buys papers for 50 cents and sells them for 75 cents, and cannot return
unsold papers.

If the newspaper seller stocks too many papers a loss is incurred. If too few papers are
stocked potential profit is lost because of the excess demand. Let s represent the number
of newspapers stocked, and X the daily demand.

a) If P is the newspaper seller’s profit for a particular stock level s, find and expression
for P in terms of s and X.

ans. 0.75x-0.5s  x<s
       0.5s-0.25x  x>s

[TrueTears]

I remember asking about this question... if my memory serves me correct I think the answers were wrong...

[khalil]

Then what were the actual answers?

[khalil]

Why does 0! = 1?

[TrueTears]

http://mathforum.org/dr.math/faq/faq.0factorial.html

[khalil]

In the 2007 Exam 1 Q7) http://www.vcaa.vic.edu.au/vce/studies/mathematics/cas/pastexams/2007/2007mmCAS1-w.pdf
the assesor's report http://www.vcaa.vic.edu.au/vce/studies/mathematics/methods/assessreports/2007/mm-mmcas1_assessrep_07.pdf fails to mention that +C is included in antideriving. Does this mean we dont have to put +C in?

Also, in the assesor's report they quote 'The instruction ‘hence’ was often ignored,' I don't see the word hence in the question. Can someone explain.

[hyperblade01]

You'll see the question says

'AN antiderivative' which implies one only. +c kinda makes it general


Badly worded, I'm sure someone else can explain it better


EDIT: 'Use the fact' is the same as 'hence', 'therefore', 'now' etc

[TrueTears]

Yes hyperblade01 is right, remember the subtle difference b/w THE anti derivative and AN anti derivative.

[khalil]

Yes hyperblade01 is right, remember the subtle difference b/w THE anti derivative and AN anti derivative.

Interesting. But if I did add C, they can't take off marks, could they?

[TrueTears]

depends, they might if they are tight, because AN anti derivative means one, not the general solution.