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Probability

The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.

14,643 Questions

What are the possible outcomes of a trial?

The possible outcomes of a trial include a verdict of guilty, not guilty, or a hung jury, where the jury cannot reach a consensus. In civil trials, outcomes can be a judgment for the plaintiff or defendant, or a settlement may occur before a verdict. Additionally, a case may be dismissed or result in an appeal depending on the circumstances. Each outcome can lead to various legal consequences, such as sentencing, fines, or further legal actions.

How many outcomes are possible if you roll 3 fair dice?

The first cube can land in 6 different ways. For each of those . . .

The second cube can land in 6 different ways. For each of those . . .

The third cube can land in 6 different ways.

All three of them can land in (6 x 6 x 6) = 216different ways.

If the three cubes are different colors, then you can tell the difference among all

of the 216 different possibilities.

But if all three cubes are the same color, then the following 6 different outcomes

all look the same to you:

2-4-6

2-6-4

4-2-6

4-6-2

6-2-4

6-4-2

The number of outcomes that look different to you would be only 216/6 = 36 .

What is a favourable outcome?

The outcome that is the top number on a fraction.

e.g. The multiples of 3 are 3 and 6 = there are 2 favourable outcomes.

Probability ( multiple of 3 ) + 2/6 = two favourable outcomes/six possible outcomes

What are the odds of a left-handed person meeting another left-handed person?

There are plenty of left handed people, so if you are left handed you'll probably meet another left handed person at some point.

Approximately 10% of the population of the United States is left-handed. That means that of every encounter between two people, one in ten will include at least on left-handed person. To find out how many will be between two left-handed people, you multiply 10% by 10%, you get 1%, or one in 100, so the odds of a left-handed person meeting another left-handed person are 1 in 100.

Your question doesn't specify "meeting for the first time"; encountering someone you already know changes things a little, since left-handedness can run in families. Also, those odds don't include meetings with more than two people, or research into facts such as there being left-handed conventions, or left-handed baseball pitchers tending to know one another. That's probably not a big deal, though, and there may be sports or occupations that favor right-handers, which balance things out.

Stages in data collection?

Data collection typically involves several stages:

  1. Planning: Define the objectives, identify the data needed, and select appropriate methods for collection.
  2. Design: Develop a detailed plan that includes tools and instruments for collecting data, such as surveys, interviews, or observations.
  3. Execution: Implement the data collection process, ensuring that data is gathered systematically and ethically.
  4. Review: Analyze and validate the collected data to ensure accuracy and reliability before proceeding with further analysis.

What are the Chances of getting a boy or a girl?

About 50/50. Slightly more boys are conceived than girls but slightly more girls make it to term than boys.

Probablity of an event occurring to the probablity that it will not occor?

Let p = probability the event will occur; and q = probability the event will not occur.

The relationship is p=1-q or q=1-p.

If a box contains three blue cards and three white cards If two cards are drawn one at a time find the probability that both cards are blue if the draws are made with replacement?

The probability of drawing two blue cards froma box with 3 blue cards and 3 white cards, with replacement, is 1 in 4, or 0.25.

The probability of drawing one blue card is 0.5, so the probability of drawing two is 0.5 squared, or 0.25.

A typical expectation in actual practice is that estimates should have a probability of being met of the time?

A typical statement in the field is the desire to "have a 95 percent probability of meeting time and cost estimates."

Given mean of 0 and deviation of 1 what is the probability that Z is greater than -1.96?

The probability of Z from minus infinity to -1.96 is 0.025. Therefore the probability of Z greater than -1.96 is 1 - 0.025 or 0.975 or 97.5%.

What is the probability of picking a card between 3 and 6 out of a standard deck of playing cards?

As phrased, this is a bit of a trick question. Each of 4 suits in a standard deck contains 2 cards between 3 and 6 (the 4 and 5 cards), for a total of 8 cards between 3 and 6. Thus the probability of any pick being a 4 or 5 is 8 out of 52, or 2:13.

If the questioner actually meant to ask about cards "from 3 to 6", which would include the 3 and 6, the odds double to 16 out of 52, or 4:13.

What is the probability of rolling 2 threes in a row with a single six sided die?

The probability of rolling a 3 with a standard die is 1 in 6. The probability of doing that two times in a row is 1 in 6 squared, or 1 in 36.

What is math used for?

  • Mathematicians do maths for fun. They dream up new abstract logical systems, and investigate the properties of those systems. They then publish their results, which are read by (mostly) other mathematicians. One hears talk of "advancing the art" and "intellectual challenge", but really fun is the best overall description.
  • The properties of an abstract mathematical system may or may not correspond to the properties of anything in the concrete world that we live in. Many of them don't.* However, professional thieves physicists and others are always on the lookout for some bit of maths which they can walk off with and use to make sense of some of their experimental data, or describe their latest theory.
  • Maths is used by scientists (physicists especially), engineers of all kinds, bankers, stock-brokers, statisticians, soldiers (artillerymen in particular), accountants, poker players and code-breakers. A list of what all these people do with it would need a small book.

* as far as we know ! A part of maths called "group theory" was thought to be just another fun thing for mathematicians to play with. Then in the 1930s (and in great secrecy) it was used to break the German "Enigma" code machine. This had an enormous impact on WW2. Group theory is now much used to make sense of elementary particles.

thats what math is used for

What is evaluate each expression?

That means to look at each statement separately and evaluate after each step.

What is an idiom for If something goes wrong it probably will?

Murphy's Law: If something CAN go wrong, it WILL go wrong (and usually at the worst possible time).

usually seen WITHOUT the part in parentheses