Probability

It is always non-negative.

The sum (or integral) over all possible outcomes is 1.

5:16

The probability is based on the second cube having 6 sides. No matter what you roll on the first cube, the chance of rolling "doubles" is 1 in 6! Now if you ask, what is the chance in rolling a specific set of doubles, the chance is 1 in 6 times 1 in 6 times, or 1 in 36 ...

1,2,3,4,5,6

With 3 coin tosses, the possible outcomes are:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

There are 8 possible outcomes and 3 of them have 2 heads. Thus:

probability = 3/8 (= 0.375)

Two independent outcomes with constant probabilities.

This means that if a newborn female is 53.8 cm in length, then she is longer than 95% of other newborn females.

You have a total of 11 letters in "mathematics" and you have 4 vowels (a,e,a,i) so the probability of drawing a vowel is 4/11.

In other words if you were to consider the vowel's to be 1's and the consonants 2's. What is the probability of drawing a "1". There would be 4 1's and 7 2's. It would be 4/11

ok I'm sure not many people will be asking this but a biased spinner is basically a spinner that is unfair or not accurate

Because probability is a measure of how likely it is that some event will occur. If there is no chance at all that the even will occur than the probability is 0. If it will occur with 100% certainty, then it is 1 or 100%

A negative number would have no meaning in terms of how likely an even is to occur?

3/5=g/30

You got a one or a four. One is the zeroeth multiple of 4. Four is the first multiple of four. Any other result, such as 8, and you are not rolling a standard die.

2/9

Empirical Distribution: based on measurements that are actually taken on a variable.

Theoretical Distribution: not constructed on measurements but rather by making assumptions and representing these assumptions mathematically.

empirical distribution is based on your observation of out comes, it is based on real data. on the other hand theoretical is base on your theory regarding the distribution and the parameters, (i.e. normal/exponential...., u=5 vs u .5....and so on)

25/36

64

5/6 0.833333333 ect. 83%

It's the same as a z-Transformation.

for all xi: (xi-mean(x)) / std(x)

Yes it is. Discrete data is something that's set. Like say you were making a line graph about renting bikes. You can only rent whole bikes there is nothing in between. You shouldn't connect points on a line graph with discrete data but some cases can be argued.

Continuous data is usually a measurement that could change like time.

The probability of at least 1 match is equivalent to 1 minus the probability of there being no matches.

The first person's birthday can fall on any day without a match, so the probability of no matches in a group of 1 is 365/365 = 1.

The second person's birthday must also fall on a free day, the probability of which is 364/365

The probability of the third person also falling on a free day is 363/365, which we must multiply by the probability of the second person's birthday being free as this must also happen. So for a group of 3 the probability of no clashes is (363*364)/(365*365).

Continuing this way, the probability of no matches in a group of 41 is (365*364*363*...326*325)/36541

This can also be written 365!/(324!*36541)

Which comes to 0.09685...

Therefore the probability of at least one match is 1 - 0.09685 = 0.9032

So the probability of at least one match is roughly 90%

since there are 6 sides to it any of them could show up, 1,2,3,4,5, and 6 could all show up unlikely

A random variable which can take qualitative values rather than numeric values. For example, the question "What colour are your eyes?" will generate qualitative answers.