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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: missemtee on September 09, 2013, 03:10:30 pm

Title: probability help
Post by: missemtee on September 09, 2013, 03:10:30 pm: I really struggle with probability! I don't understand what I'm doing or why I'm doing it. Please help explain and answer this question.I got part a and d but not b and c. I know it sounds so simple but I don't know how to do it :( THANK YOU!! :)

The santaroos have 3 soccer teams, A,B of and C, entered in the interschool championships. Each team is entered in a seperate division. The probability of each team winning their particular final is given as follows:
Pr(Team A wins)= 1/2
Pr(Team B wins)= 1/3
Pr(Team C wins)= 3/4
Find the probability that:

a) none of the santaroos teams win
b) one of the santaroos teams win
c) two of the santaroos teams win
d) each of the santaroos teams win their particular final
Title: Re: probability help
Post by: b^3 on September 09, 2013, 03:27:22 pm: For part b, look at what ways we can get only one winning. I.e. To satisfy what we're looking for we can have three situations.
A wins, B and C loses.
B wins, A and C loses.
C wins, A and B loses.
The sum of the probability of those events will give you the probability of only one winning.
So for the first one, the probability that B loses is one take the probability that B wins, so we have
$\frac{1}{1}\times \frac{2}{3} \times \frac{1}{4}$ .
Do that for all three and then add them up.

A similar situation goes for part c.
How can we have 2 teams winning?
A and B wins, C loses.
A and C wins, B loses.
B and C wins, A loses.

Hope that helps :)

EDIT: Also note that this works because each of the events are independent, since the teams are in separate divisions.