Probability

Carl Gauss wrote Disquisitiones Arithmeticae, which is regarded today as one of the most influential books written in math, and is the first book written on number theory.

For normal dice, and assuming "combined" refers to the sum, the answer is 7.

Yes.

There is no simple answer to this question because the genders of children depend on the parents genes and age and so are not independent events. Also, the probabilities of the two genders are not equal. Further, some of the children may be identical twins or triplets.

Assuming, however, that the genders are independent, the answer is 0.3872, approx.

Rolling a six with a die or not rolling a six.

Yes. The probability of this occurring is 0.520 = 0.00000095367 or 1 in 1,048,576 thus you are more likely to do this than win the lottery

Check out the link. Any of those shapes, except the square, works.

The raw score is any value that is observed.

They will justify their interest in your recent activities.

48

A set of outcomes are called results. All possible outcomes are referred to as the sample space.

It depends on what variable the probability ratio was for! The random variable could have been the number of heads minus the number of tails, for example.

This sounds like a joke question. If you toss a coin in a train, it lands in the train. If you toss it out the window, or otherwise off the train, it lands on whatever is out there.

On the other hand, assuming this is not a joke, the coin will land where it would if you tossed it if the train were stationary. In other words, the coin is moving at the same velocity as the train before the coin toss, and since that part of its momentum is preserved through the toss, it will land, relative to the train, in the same place. This assumes, of course, that the train is not changing speed during the coin toss, that the windows are not admitting a wind, and so on.

1/3 of course. If it's not one third, what is it?

Less likely means that it has more of a chance not to happen.

To determine the number of possible outcomes on a spinner, you need to know how many distinct sections or segments the spinner has. Each segment represents a different possible outcome. For example, if a spinner is divided into 8 equal sections, there are 8 possible outcomes. If you provide more details about the spinner, I can give a more specific answer.

There are an infinite amount of ways.

an event

You can't be sure to get the 50/50 ratio of heads and tails. Each time will be a trial & error.

Ones that are near the population mean.

With 2 6-sided dices there are 6x6=36 combinations (6 for the first dice, 6 for the second dice)

Let put the question this other way: how many combinations with a total more than 8, namely 9, 10, 11 or 12 ?

9: 4 combinations: 4-5 or 5-4 or 6-3 or 3-6

10: 3 combination: 5-5 or 6-4 or 4-6

11: 2 combinations: 6-5 or 5-6

12: 1 combination: 6-6

So there are 10 combinations for "more than 9" thus there are 36-10=26 combinations for "less or equal to 8".

The likelihood of increasing behavior is often associated with reinforcement, which can be positive or negative. Positive reinforcement involves providing a rewarding stimulus after a desired behavior, increasing the chances of that behavior being repeated. Negative reinforcement entails the removal of an unpleasant stimulus when the desired behavior occurs, also promoting its recurrence. Both forms of reinforcement play a crucial role in shaping and enhancing behavior in various contexts, such as education and behavior modification.

The are more ways to roll a 6 (five ways) than to roll a 4 (three ways).

2 out of 6.

16/52 because there are 13 hearts and 4 kings but one of the kings is a heart. and there are 52 cards in one full deck.