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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 is the probability of drawing a seven of spades?

Probability of drawing a seven of spades, from a 52 card deck, is 1/52.

How do find the probability of A complement given B complement?

With the information that is available from the question, it is impossible.

What does total probability equal?

For any particular trial, the total probability is 1.

Why is probability important to a scientist?

Some but not all scientific models are based on the ability to determine the likelihood that a given experimental outcome has happened by chance alone. If you have an accurate understanding of how the variables in the experiment change when nothing in particular is affecting them, then you have a way to establish some confidence that your outcome is the result of your experimental procedure and not the result of purely random events. The experimental 'lingo' is that the researcher has to determine if the 'Null Hypothesis' can be rejected. The Null Hypothesis is that the experimental outcome is not significantly different from what you would expect if the experiment had no effect at all.

As an example, if the probability in the natural world is that some event will happen by chance only one tenth of one percent of the time, then when I observe that event as my experimental outcome, I can be reasonably sure that my procedure has brought about the event; it is so unlikely that it happened by chance. It is not perfect, but few scientific procedures are. This also highlights the importance of replicating studies or of doing meta-analyses of experimental data gathered in many experiments to further reduce the likelihood that observed outcomes are nothing more than chance events.

What is probability that 2 persons sharing same birth date?

If you assume that birth dates are uniformly distributed over the year (they are not), and you ignore leap years, then the probability of two people selected at random, share a birthday is 1/365.

How many zeros are possible factorial 10 to the power factorial 10?

To calculate the number of zeros in a factorial number, we need to determine the number of factors of 5 in the factorial. In this case, we are looking at 10 to the power of 10 factorial. The number of factors of 5 in 10! is 2 (from 5 and 10). Therefore, the number of zeros in 10 to the power of 10 factorial would be 2.

How would you explain the concept of probability to a child?

Start with examples like flipping a coin, rolling a die or spinning a dreidel. Then explain in terms they understand. That depends very much on the age of the child.

What is the probability of your birthday falling on a weekend?

The answer depends on where in the world you are. In some places, where hospital [or maternity unit] births are more popular, the medical staff prefer to deliver babies during weekdays so that they can have time with their own families at weekends. As a result, the distribution of births is not uniform across days of the week.

What is Probability of Flipping a coin five times in a row and having it land on heads?

The probability of getting a heads on the first flip is 1/2.

Similarly, the probability on each subsequent flip is 1/2, since they are independent events.

The probability of several independent events happening together is the product of their individual probabilities.

How many possible outcomes would there be if a coin is tossed?

2, there could only be two outcomes. Heads or tails

As in any experiment you need to define a valid toss. So if you are examining the number of heads and tails you would limit the outcomes to these two states. However, in a real world experiment there may be a condition where the coin landed on a uneven surface and was tilted in some way. The number of tilted ways is infinite. You could also have the coin land on its edge which is unlikely but possible.

What is the probability of choosing a jack at random from a pack of cards?

Assuming a 52 card deck, 4 jacks / 52 cards or probability of 4/52 or 1/13 or 0.077.

How many positive integers less than 100 can be written using digitals 1 3 5 7 9 if digits can be repeated?

1-digit number: 5 possibilities

2-digits number: 5 x 5 = 25 possibilities

So there are 30 numbers.

Which are the four face-cards in a poker deck?

There are 12 face cards in a standard 52-card deck, a jack, a queen and a king of each of the four suits.

When are two events NOT mutually exclusive?

When there is at least one outcome in which both events occur simultaneously.

Event A: The next person to enter the mall is male

Event B: The next person to enter the mall is married

If a married man walks in next, then both events occur.

What is the probability of not rolling a sum of 2 4 or 6 with two fair dice?

There are 36 possible outcomes when throwing 2 dices : 6 for the first dice (1,2,3,...6) and 6 for the second dice

Let say that in the sums below the first number is the result of the first dice and the second number is for the result of the second dice:

2 = 1 + 1: 1 possibility

4 = 2 + 2 = 1 + 3 = 3 + 1: 3 possibilities

6 = 1 + 5 = 5 + 1 = 2 + 4 = 4 + 2 = 3 +3: 5 possibilities

1 + 3 + 5 = 9 possibilities to get 2 or 4 or 6

So the probability to get a sum of 2 or 4 or 6 is 9/36=1/4

And the probabilty of NOT rolling a sum of 2 or 4 or 6 is 1-1/4=3/4

What does probability of one mean?

It means you have 100% chance or certain.

Why are experimental probabilities sometimes very different from theoretical probabilities?

A perfect example of how theories are tested ! Theory predicts the outcome

of the experiment, and the purpose of the experiment is to test the theory.

If the outcome of the experiment is appreciably different from the one predicted

by the theory, (and if the experiment itself was valid), then the prediction is flawed,

and the theory must be either tweaked or trashed.

What is the probability of picking a two replacing it in the deck of cards and then picking a king?

there is a 1 in 13 chance of picking a 2 in a deck of cards, then picking a king afterwards, its also a 1 in 13 chance, but together, theres a even slimmer chance.

What is the probability that a far six-sided die rolled until the first 5 occurs on the tenth roll?

Assuming that the die is fair rather than far, the probability is (5/6)9(1/6) = 1,953,125/60,466,176 = 0.0323 approx.

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