VCE Maths questions help (1 Viewer)

[boredsatan]

Is "nor" the same as "and" in probability?

 

[boredsatan]

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]

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]

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]

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]

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]

The second one is always correct. The first is only correct if Pr(A and B) = 0 (basically mutually exclusive events).

If you use the second formula for P(A and B), is that wrong?
Thanks

 

[InteGrand]

If you use the second formula for P(A and B), is that wrong?
Thanks

It's not wrong (as I said, the second is always correct).

 

[boredsatan]

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?

 

[boredsatan]

It's not wrong (as I said, the second is always correct).

Thanks

 

[InteGrand]

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).

 

[InteGrand]

The answer said 24/38. Do you now how it's worked out?

You need to use the definition of conditional probability and make an independence assumption. See my above post.

 

[boredsatan]

-y≥ - x + 2
y≤1x - 2

Are these the same?

 

[jazz519]

-y≥ - x + 2
y≤1x - 2

Are these the same?

Yep

 

[pikachu975]

-y≥ - x + 2
y≤1x - 2

Are these the same?

Yep remember that dividing or multiplying by a negative swaps the sign

 

[He-Mann]

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.

§§§

 

[dan964]

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

§§§

we will give him the benefit of the doubt...

 

[boredsatan]

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]

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

 

[boredsatan]

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

§§§

Can you please stop the insults