Member: Alan

PabloDons:
Is there a way to calculate the chance to get a 6 on a dice after throwing it 6 times? the only way I can think of is setting up all possible combinations which would be insanely long, Example:
111111 111111
111111 111111
111111 111111
111111 111111
111111 222222
123456 123456 etc.
I have tried my hardest but couldn't figure out a formula.
any help is appreciated
- Pablo

Your question has more than one interpretation!

If you mean: "What is the probability of getting at least one 6 in six throws of the dice" then this is just 1 - the probability of getting no sixes.
The probability of getting no six for the first die is 5/6.
The probability of getting no six for either the first or second die is (5/6)*(5/6) or 5 ²/6 ²
The probability of getting no six for any of the first three dice is (5/6)*(5/6)*(5/6) or 5 ³/6 ³
Continuing this way, the probability of getting no sixes for any of the six dice is 5 ⁶/6 ⁶
Hence, the probability of getting at least one six is 1- 5 ⁶/6 ⁶

1-5^6/6^6

If you mean "What is the probability of getting exactly one 6 in six throws of the dice" then
The probability of one particular die getting a 6 and all the others getting no sixes is (1/6)*(5 ⁵/6 ⁵)
But there are 6 dice each of which could be the one that falls as a 6, so the probability is 6*(1/6)*(5 ⁵/6 ⁵) or 5 ⁵/6 ⁵

5^5/6^5

If you mean something else then you'll need to specify exactly what!

AlanMar 5, 2014

+33614

ABDULLAH:
If $10,000 is invested at an interest rate of 2% per year, compounded semiannually, find the value of the investment after the given number of year. 4 year

The formula for calculating compound interest is F = P(1 + r/n) ^nt where P is the amount invested ($10,000), r is the interest rate expressed as a fraction (0.02), n is the number of times compounded in a year (2), t is the number of years invested (4) and F is the future value (i.e. the amount the investment is worth after t years). Have a go at the calculation now you have this information.

AlanMar 5, 2014

+33614

bookstar:
ln(e^-9x)

ln(e ^-9x) is just -9x. This is because ln is the natural or Napierian logarithm - that is, the logarithm to the base e. In general log _b(b ^a) = a (where log _b is logarithm to the base b). In your example, b is e and a is -9x.

AlanMar 5, 2014

+33614

reinout-g:
ayubbadman:
x2+2xy+y2

Your notation might lead to some misinterpretation but I think what you mean is x^2 + 2xy + y^2 which means x ² + 2xy + y ²

//You can get this second one by using the [sup']2[/sup'] command without the '

We can factorize this to (x ²+y ²)

Factoring is something which is not easy to explain, but maybe this website will help you.

http://www.purplemath.com/modules/factquad.htm

I think you made a slight typo here reinout. You probably meant: We can factorize this to (x+y) ²

AlanMar 4, 2014

+33614

Melody:
Alan:
Melody:
*
Would like to comment on, or add to anything that I have said regarding communication with Andrew Massow.
If so, this would be an appropriate place to have your say.

Melody.

I've noticed that the [sup] button doesn't work in Preview mode (I haven't checked any of the others).

Hi Alan,
The sup works alright in preview mode for me.
Why don't you try it again.
Melody.

Ok, it works. I was looking at the wrong part of the Preview! Thanks Melody.

AlanMar 4, 2014

+33614

Melody:
*
Would like to comment on, or add to anything that I have said regarding communication with Andrew Massow.
If so, this would be an appropriate place to have your say.

Melody.

I've noticed that the [sup] button doesn't work in Preview mode (I haven't checked any of the others).

AlanMar 4, 2014

+33614