Probability

you can just ask the question on ask .com

Theoretical probability

1/365 = 0.00274

When you use linear regression to model the data, there will typically be some amount of error between the predicted value as calculated from your model, and each data point. These differences are called "residuals". If those residuals appear to be essentially random noise (i.e. they resemble a normal (a.k.a. "Gaussian") distribution), then that offers support that your linear model is a good one for the data. However, if your errors are not normally distributed, then they are likely correlated in some way which indicates that your model is not adequately taking into consideration some factor in your data. It could mean that your data is non-linear and that linear regression is not the appropriate modeling technique.

12, because you can only get it one way: 6+6=12

And 2, because get it one way: 1+1=2.

4.5%

1-52

In a standard deck of 52 cards.

Probability of drawing a spade: 4 suits, only 1 is spade.

Each suit contains A-10 (10 cards) + K + Q + J (3 cards)

13 cards in each suit.

There are 13 cards in the spades suit.

You have a 13/52 chance of drawing a spade on your first draw.

Probability of drawing a 5: there are only 4 5's in the deck.

3/52 chance of drawing a 5. (one 5card per suit that is not spades)

13/52 + 3/52 = 16/52 = .3076 or 30.8% chance of drawing a 5 or a spade on your first pull.

----------------------------------------------------------------------------------------------------------- ANSWER: Depends on the first supervisor's age and interests. -----------------------------------------------------------------------------------------------------------

5 over 2, i.e. the number of combinations of 2 elements from 5. To understand this you need to study a little bit of combinatorics (how to count combinations): you might want to start from the lectures on combinatorics at statlect.com.

I believe you meant to ask: What distinguishes a random sample from a non random sample? A random sample means the selection or sampling from the population is by chance. Looking at the data, one might not be able to tell if the sample is random or selective. Consider a marketing survey which is included everytime you buy an item online. Random or non-random? It is a survey of recent customers, and probably a pretty good one. But it is not a random selection of all customers who have made purchases with clients.

1:24 one in 24 rolls

The question is rather ... short. You are probably referring to the Regular Exponential Class (REC). A density function is said to be a member of REC if it can be decomposed as follows (LaTeX code, since I don't know how to write this stuff here):

f(x;s)=c(s)h(x)exp[\sum_{j=1}^{k} q_j(s) t_j(x)] for x \in A and zero otherwise. Here, s is a vector of k unknown parameters (s_1, ... , s_k). Moreover, the following conditions need to be satisfied: the parameter space needs to be compact (i.e. for all i, we have fore each parameter that a_i \leq s_i \leq b_i, for a_i and b_i constants, where also infinity is allowed), also, the set A over which the density is strictly positive should not depend on the parameters s, the functions q_j should be non trivial, functionally independent, and continuous functions of the parameter, and the last condition is that the derivatives t'_j(x) are linearly independent continuous functions of x over A (with a similar condition existing for discrete random variables).

Why we care about REC? Various reasons: e.g. we can then immediately derive a set of complete and sufficient statistics, or construct uniformly most powerful tests for one-sided hypothesis testing.

When considering the probability of two different events or outcomes, it is essential to clarify whether they

are mutually exclusive or independent. If the events are mutually exclusive, then the probability that either

one or the other will occur equals the sum of their individual probabilities. This is known as the law of

addition.

If, however, two or more events or outcomes are independent, then the probability that both the first and

the second will occur equals the product of their individual probabilities. This is known as the law of

multiplication.

There is a one in two chance of tails every time, rewritten as 1/2

The probability of tail 3 times in a row is 1/2 x 1/2 x 1/2= 1/8.

So the answer is one in eight, or 12.5%

130 instances of 3 heads out of 1024 total possible outcomes=130/1024=0.126953125

at least one tail

Probability, Severity, and Exposure

Washing hands after patient contact; using gloves when touching blood, body fluids, secretions, excretions, and contaminated items;.

It depends on what exactly the conditions are. If you mean from a 52 card deck, drawing one card right after the other, then the chance that they will be those two cards in that exact order is 1/52 * 1/51. This is pretty much a percent of a percent. .00038, or about 4 percent of a percent.

Heptagons have seven sides.

In a single toss? zero. In two tosses, well that's a different question. Possible combinations are TT, HT, TH and HH, of which 2 of the 4 are one head and one tail. So probability is 0.50 in two tosses.