VCE Maths questions help (1 Viewer)

boredsatan

Member
Joined
Mar 23, 2017
Messages
572
Gender
Male
HSC
1998
There are two friends, peter and sally. Their respective probabilities of being alive in 40 years time are 0.7 and 0.8. What is the probability that Sally is alive in 40 years time, given that one of them is alive then?
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
P(a u b) = P(a) + P(b)
P(a u b) = P(a) + P(b) - P(a and b)
which formula is correct?
I see both formulas being used in calculations
The second one is always correct. The first is only correct if Pr(A and B) = 0 (basically mutually exclusive events).
 

fluffchuck

Active Member
Joined
Apr 29, 2016
Messages
257
Location
Sydney
Gender
Male
HSC
2017
Uni Grad
2021
There are two friends, peter and sally. Their respective probabilities of being alive in 40 years time are 0.7 and 0.8. What is the probability that Sally is alive in 40 years time, given that one of them is alive then?
If P(Sally alive) = 0.8 and P(Peter NOT alive) = 0.3,

Then the probability that only Sally is alive in 40 years time is given by
P(Sally alive) x P(Peter NOT alive) = 0.8 x 0.3 = 0.24
 

dan964

what
Joined
Jun 3, 2014
Messages
3,479
Location
South of here
Gender
Male
HSC
2014
Uni Grad
2019
boredofsatan, just 2 friendly reminders...

1. It may be helpful for you to demonstrate what you understand in terms of the concepts, maybe show working or attempts on the question. This is to give other users assurance/evidence, that they are not just for instance doing your homework etc. for you, and that you are actually learning and grappling with the concepts.

2. Also, do not excessive bump your question if it hasn't been answered yet. (and sometimes you come across as "swamping" with lots of questions, ask one or two at a time)

thanks
dan
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
572
Gender
Male
HSC
1998
boredofsatan, just 2 friendly reminders...

1. It may be helpful for you to demonstrate what you understand in terms of the concepts, maybe show working or attempts on the question. This is to give other users assurance/evidence, that they are not just for instance doing your homework etc. for you, and that you are actually learning and grappling with the concepts.

2. Also, do not excessive bump your question if it hasn't been answered yet. (and sometimes you come across as "swamping" with lots of questions, ask one or two at a time)

thanks
dan
No problem
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
572
Gender
Male
HSC
1998
If P(Sally alive) = 0.8 and P(Peter NOT alive) = 0.3,

Then the probability that only Sally is alive in 40 years time is given by
P(Sally alive) x P(Peter NOT alive) = 0.8 x 0.3 = 0.24
The answer said 24/38. Do you now how it's worked out?
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
There are two friends, peter and sally. Their respective probabilities of being alive in 40 years time are 0.7 and 0.8. What is the probability that Sally is alive in 40 years time, given that one of them is alive then?
You need to make an assumption about the dependence of the lives, otherwise there is not enough information to do the question. Since we aren't told anything about it, you probably should assume the lives are independent.

Then letting A denote the event that one of them (i.e. at least one of them) is alive in 40 years, and S and P respectively for the events that Sally, Peter are alive in 40 years, the probability we are asked to find it Pr(S|A).

This is equal to Pr(S ∩ A)/Pr(A).

Now, A = S ∪ P (i.e. A occurring means Sally lives or Peter lives (remember, unions effectively represent "or")), so

Pr(A) = Pr(S) + Pr(P) – Pr(S ∩ P).

The probabilities on the RHS here are either given or can be calculated using our independence assumption.

The last thing we need is Pr(S ∩ A). This is quite easy to find! See if you can do so (think about what the event S ∩ A is).
 

He-Mann

Vexed?
Joined
Sep 18, 2016
Messages
278
Location
Antartica
Gender
Male
HSC
N/A
boredofsatan, just 2 friendly reminders...

1. It may be helpful for you to demonstrate what you understand in terms of the concepts, maybe show working or attempts on the question. This is to give other users assurance/evidence, that they are not just for instance doing your homework etc. for you, and that you are actually learning and grappling with the concepts.

2. Also, do not excessive bump your question if it hasn't been answered yet. (and sometimes you come across as "swamping" with lots of questions, ask one or two at a time)

thanks
dan
I guarantee you boredsatan will not follow these. __________this is planned. He will follow these rules to prove me wrong.

§§§
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
572
Gender
Male
HSC
1998
I've gone through this but still feel confused, that's why i am asking
How do you know if the equilibrium position is y = or x =
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
572
Gender
Male
HSC
1998
maths.gif

To find the area of this shape, do you need to minus the line of the semicircle that intersects with the rectangle?
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top