ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Tea.bag on September 04, 2008, 06:33:27 pm

Title: Probability
Post by: Tea.bag on September 04, 2008, 06:33:27 pm: DOnt get it.

It is known in a certain town that on any evening 35% of people will not be at home. What is the probability that a telemarketer will need to make five phone calls before finding someone at home on the sixth call?
Title: Re: Probability
Post by: Collin Li on September 04, 2008, 06:36:09 pm: We want this sequence of events:

FFFFFS,

where F = fail, S = success

$p = (0.35)^5\times(0.65) = 0.003413921875$
Title: Re: Probability
Post by: bucket on September 04, 2008, 11:15:46 pm: tree diagrams help heaps with these things.
Title: Re: Probability
Post by: excal on September 05, 2008, 12:23:54 am: Quote from: bucket on September 04, 2008, 11:15:46 pm
tree diagrams help heaps with these things.

Yeah, but you don't *need* them unless you're dealing with Markov chains (that is, where the posterior probabilities are different depending on the prior probabilities).

As coblin decuded, for independent events F and S, $P(F \cap S) = P(F) \times P(S)$

$\therefore P(F \cap F \cap F \cap F \cap F \cap S) = P(F)^5 \times P(S) = (0.35)^5 \times 0.65 = 0.0034$
Title: Re: Probability
Post by: Collin Li on September 05, 2008, 12:32:28 am: Hehe, probably don't want to draw a 5-step tree diagram:

$2^5 = 32$ branches :P
Title: Re: Probability
Post by: excal on September 05, 2008, 12:42:03 am: Quote from: coblin on September 05, 2008, 12:32:28 am
Hehe, probably don't want to draw a 5-step tree diagram:

$2^5 = 32$ branches :P

Well...there's that too :P
Title: Re: Probability
Post by: bucket on September 06, 2008, 12:15:00 am: you only need the initial and the transition part lol.