Statistics

The probability of getting 5 on one toss of a pair is 1/9. The most probable number of fives you will get after 42 tosses is 4 or 5.

Add the probabilities of getting 5 four, five, six, seven, eight etc times out of 42 tosses. By the time you get to 15 times, the probability will be very small and you can quit adding them up.

The probability of rolling 5 four times is (1/9)^4*(8/9)^38*42!/(38!*4!)

= 119,930*1.524*10^-4*1.138*10^-2

= 0.20803

The probability of rolling 5 five times is (1/9)^5*(8/9)^37*42!/(37!*5!)

= 8.507*10^5*1.6935*10^-5*1.2804*10^-2

= 0.18447

I am not going to continue this because it would take half the night, but you get the idea.

There is an easier way to do this that just occurred to me. It will give the same answer. Here it is:

Add the probabilities of getting 5 zero, one, two or three times, and subtract that from 1.

The probability of never getting five is (8/9)^42 = 0.007105

The probability of getting 5 only once is (1/9)*(8/9)^41*42 = 0.037304

The probability of getting 5 twice is

(1/9)^2*(8/9)^40*(42*41*/2) = 0.095591

Now YOU compute the probability of getting 5 three times. Add that to the probabilities above and subtract the sum from one. You should end up with a number around 0.6.

That will be the answer.

The mean is the average; the total of the members of the set divided by the number of members n the set.

6

Any time

Expressed as a percentage, 25/88 x 100 = 28.409 recurring (that is, 28.4090909...) percent.

Since there are six sides on a die, the odds of rolling a 4, or any digit for that matter is 1/6

It is 97.

It is an equation and the value of n is 5

Therefore: I/10 = 1/10

432 + 759 = 1191

a bar graph

nCr = n!/r!(n-r)! = 4

I'm using the combination formula where the place of the digits is not important No if the place

for instance the combination 312 is the same as 213.

But I think you are asking for a permutation instead where the placements of the digits are also important. So it would actually be 4!/(4-3)! or 24.

In a permutation the place is significant

i.e. 312 and 213 are distinct even though they have the same 3 digits.

the spin quantum number has only two possible values__(+ 1/2 & -1/2)

non

Because they are both measures of the same characteristic - the central tendency.

In a civilized culture whose citizens are accustomed to fundamental human rights

and the rule of law, one must hope that it's vanishingly small.

14

Nothing, since there is no such term. Check your notes and resubmit your question.

impossible

There is no such number, although I am struggling to prove it.

Area is calculated in _dimensions, and volume is calculated in_dimensions?

1 out of 4 is a statistic. Written in a different format it can be a ratio or a percent.

Many aspects of mathematics are not man-made. For example, the ratio of the circumference of a circle and its diameter will be pi, wherever it is. The inverse square laws for electromagnetic attraction (or repulsion) are universal. So, mathematics exists without people so no person can claim to have made it.