## January 13, 2007

### Scribe Post

Okay, today Mr.K started and finished off, with the following questions:

1)Tickets numbered 3,6,9,12,15 and 18 are placed in Box A. Tickets numbered 6,12,18,24 and 30 are placed in Box B. A ticked is chosen at random from each box. Find the probability:

a)That both tickets have the same number?

First find the numbers that are in both Box A and Box B. You will see that only 6,12, and 18 are in both Box A and Box B. Then calculate the probability for each, as shown:

P(A6B6)=(1/6)(1/5)= (1/30)
P(A12B12)= (1/30)
P(A18B18)= (1/30)

(1/30)+(1/30)+(1/30)= (3/30)= (1/10)

Therefore the probability that both numbers are the same is (1/10).

b) That there are different numbers on the two tickets?

This question is simple to answer, because we have just figured out how many times the numbers will be the same and it was (1/10), so now all we have to do is subtract this fraction from 1, resulting in the probability of the numbers not being the same.

1-(1/10)= (9/10)

2)John uses Google 50% of the time, Lycos 30% of the time and Altavista 20%.If he is using Google, there is a 40% chance he is searching for info about cell phones. If he's using Lycos or Altavista the probability he is researching cell phones is 30%.

First we should create a tree to organise our information, and making the question more easier to calculate. SORRY BUT MY PICTURE WILL NOT LOAD AT THE MOMENT, I will quickly look into it and post it as soon as possible.

a)What is the Probability that John decides for info about cell phones?

This will be simple we just need to look at our tree (which i currently don't have up so the change to this question will be made once i clear up my problem.)

b)You see John looking at a website that is not about cell phones. What is the probability he used Google to find it?

P(G/NCP)= (P(GNCP))/(P(GNCP)+ P(LNCP)+P(ANCP)
=(30/100)/((30/100)+(21/100)+(14/100))
=(30/100)/(65/100)
=(30/100)X(100/65)
=(3000/6500)
=(3/65)
=4.6%

Therefore the probability he used Google is 4.6%

*P(G/NCP) meaning: prob. used Google but not for cell phones.
*P(GNCP) meaning: prob. used Google not for cell phones.
*P(LNCP) meaning: prob. used Lycos not for cell phones.
*P(ANCP) meaning: prob. not used Altavista.

3)The letters AADKRRV are written on separate pieces of paper and placed in a bag. If they are drawn from the bag at random, what is the probability that the order of the letters spell AARDVARK?

There where many ways to calculate this problem. I will show you how I have completed the question.

First I reflected on the unit on Counting, and the question became simple. A method we where tought involved lines and multiplying the factorials that go in them. Then I applied it to my knowledge of going about solving probability questions. I came up with this:

3!/8 chances of A 1st.
2!/7 chances of A 2nd.
1!/6 chances of R 3rd.
1!/5 chances of D 4th.
1!/4 chances of V 5th.
1!/3 chances of A 6th.
1!/2 chances of R 7th.
1!/2 chances of K 8th.

Then I simplified the answer and this is what I got:

(3!2!)/(8!)

4)Two traffic lights operate independently. The probability that the first is red is 0.4. The prob. that the second is red is 0.7. What's the probability that neither are red?

P(NR1)= 0.6
P(NR2)= 0.3

(0.6)(0.3)=.18

Unfortunately the Big Space has come back,heh, I was able to kinda fix but its still there.

THE NEXT SCRIBE IS THE JESSICA THAT HAS'NT DONE 3 SCRIBES YET.