Question about Casio FX-115ES Scientific Calculator

# Binomial function how do i use the binomial function on my calculator? (what do I enter in order to solve a problem)?

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• Casio Master

Hello,

The binomial probability distribution is defined as
P(r;p;n) =(nCr)(p^r)*(1-p)^(n-r)
where n is the number of trials, p the probability of success, and r the expected result.

Let n=20, r=7, p=0.15 ( I do not know wether this exemple has any meaning in the context of your problem, but you have to enter values that mean something to you. I am only showing you the key strokes

To enter 20C7 you press 20 [SHIFT][nCr]7 ;
To enter 0.15 to the power 7 you type 0.15[X to ] 7 the key is between
[x²] and [log]

To enter (1-0.15) to power 20-7, you type 0.85 [X to] 13
With [*] standing for multiplication key , and [X to] the raise to power key, the exemple above can be entered as

( 20 [SHIFT][nCr] 7) [*] ( 0.15 [X to] 7 ) [*] ( 0.85 [X to] 13 ) [=]

Here is a screen capture to show you what it looks like. However on this calculator the combination 20 [SHIFT][nCr] 7 is represented as nCr(20,7).

Hope it helps

Posted on Nov 15, 2009

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Posted on Jan 02, 2017

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Use the quadratic formula, or factor the quadratic polynomial. Once factored into a product of two first degree binomials, the roots are obtained by setting (in TURN) each binomial factor equal to zero.

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### Texas 30XIIB binomial cdf

The only known equation for the cumulative binomial distribution is the sum of the individual binomial probabilities. Some more sophisticated (and more expensive) calculators have that equation built in, but the 30xii does not.

If n>30 and n*p>5 and n*(1-p)>5 then you can approximate the cumulative binomial with the normal probability function, but again the 30xii does not have that built in.

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Do you have a question about the binomial probability distribution function or the binomial cumulative distribution function?

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Use the key next to which is the marking nPr, for permutations, and the key nCr for combinations. In all probability, the functions are accessed by pressing the SHIFT key first. To use these functions, enter the larger number (n), press the key or key sequence then enter the smaller number (r).
I cannot say about the binomial function (I do not have the hardware with me), and do not really want to second guess you: you do not specify the type of problems you have in mind.

Aug 04, 2011 | Casio FX-300MS Calculator

### TI-89 Titanium: I want to solve a Binomial Theorem problem (x+y)^6 how would i go about solving this in the calculator?

Using elementary algebria in the binomial theorem, I expanded the power (x + y)^n into a sum involving terms in the form a x^b y^c. The coefficient of each term is a positive integer, and the sum of the exponents of x and y in each term is n. This is known as binomial coefficients and are none other than combinatorial numbers.

Combinatorial interpretation:

Using binomial coefficient (n over k) allowed me to choose k elements from an n-element set. This you will see in my calculations on my Ti 89. This also allowed me to use (x+y)^n to rewrite as a product. Then I was able to combine like terms to solve for the solution as shown below.
(x+y)^6= (x+y)(x+y)(x+y)(x+y)(x+y)(x+y) = x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6

This also follows Newton's generalized binomial theorem:

Now to solve using the Ti 89.

Using sigma notation, and factorials for the combinatorial numbers, here is the binomial theorem:

The summation sign is the general term. Each term in the sum will look like that as you will see on my calculator display. Tthe first term having k = 0; then k = 1, k = 2, and so on, up to k = n.
Notice that the sum of the exponents (n ? k) + k, always equals n.

The summation being preformed on the Ti 89. The actual summation was preformed earlier. I just wanted to show the symbolic value of (n) in both calculations. All I need to do is drop the summation sign to the actual calculation and, fill in the term value (k), for each binomial coefficient.

This is the zero th term. x^6, when k=0. Notice how easy the calculations will be. All I'm doing is adding 1 to the value of k.

This is the first term or, first coefficient 6*x^5*y, when k=1.
Solution so far = x^6+6*x^5*y

This is the 2nd term or, 2nd coefficient 15*x^4*y^2, when k=2.
Solution so far = x^6+6*x^5*y+15*x^4*y^2

This is the 3rd term or, 3rd coefficient 20*x^3*y^3, when k=3.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3

This is the 4th term or, 4th coefficient 15*x^2*y^4, when k=4.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4

This is the 5th term or, 5th coefficient 6*x*y^5, when k=5.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5

This is the 6th term or, 6th coefficient y^6, when k=6.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5+y^6

Putting the coefficients together was equal or, the same as for when I used the expand command on the Ti 89.

binomial coefficient (n over k) for (x+y)^6
x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5+y^6

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### When i enter the binomial probability formula into the casio fx-115es it will not operate. it says that the problem lies in the (n-X)!X! part of the formula. I'm writing everything exactly the way it is in...

You may be writing the expression as they appear in the formula, but the problem stems from the fact the factorial function increase rather rapidly and you cannot calculate the factorials of numbers larger that 69 which is the limit of the calculator.
However if you use the built in Combination function nCr, you will avoid the problem. In the binomial function, the n!/(r!(n-r)!) factor can be replaced by nCr or nC(n-r).

Do not use the explicit form with the factorials because you will get an overflow.

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### Binomial function in calculator fx-911ES

Hello,

The binomial probability distribution is defined as
P(r;p;n) =(nCr)(p^r)*(1-p)^(n-r)
where n is the number of trials, p the probability of success, and r the expected result.

Let n=20, r=7, p=0.15 ( I do not know wether this exemple has any meaning in the context of your problem, but you have to enter values that mean something to you. I am only showing you the key strokes

To enter 20C7 you press 20 [SHIFT][nCr]7 ;
To enter 0.15 to the power 7 you type 0.15[X to ] 7 the key is between
[x²] and [log]

To enter (1-0.15) to power 20-7, you type 0.85 [X to] 13
With [*] standing for multiplication key , and [X to] the raise to power key, the exemple above can be entered as

( 20 [SHIFT][nCr] 7) [*] ( 0.15 [X to] 7 ) [*] ( 0.85 [X to] 13 ) [=]

Here is a screen capture to show you what it looks like. However on this calculator the combination 20 [SHIFT][nCr] 7 is represented as nCr(20,7).

Hope it helps

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Yes, eleven million is rather extreme for the binomial distribution. For this large a value the binomial distribution is sufficiently indistinguishable from the normal approximation.

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