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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

How tall would a house of card be if you used a fifty-two card deck?

Depends on the architectural design. There could be 1 to n stories (levels) in the house. The cards could be laid on the short or long side. The angle at which the cards are leaned toward each other could differ.

(I think he meant using the original Pyramid type stacking)

Why Central Limit Theorem does not work for sample max?

Because other than in a degenerate case, the maximum of a set of observations is not at its centre! And the theorem concerns the distribution of estimates of the central value - as the name might suggest!

What is the probability of rolling a 1 or a 5 on two dice?

It is 1 - Prob(not rolling a 1 nor a 5 on either die)

(4/6)2 = (2/3)2 = 4/9 = 0.444... recurring.

When 2 dice are rolled what is the probability of getting a 5?

If you want 5 on both dice then it would be 2 out of twelve. If you want just 5 on one, 1 of six.

Pay attention in school next time! :p

What are the possibities for the intersection of a triangle and a paralleogram in a plane?

Depending on their sizes and orientation, any shape from a triangle to a dodecagon.

Why must there be a probable cause before a warrant is issued?

For the "probable cause" that a criminal event has, or is about to occur, and by serving the warrant (search or arrest) the crime can be solved or prevented.

Probable Cause (partial definition): " . . is more than mere suspicion but less than the amount of evidence required for conviction."

Carmen flips two nickels at the same time. Is the probability of getting two heads the same as that of getting one head and one tail?

No it is not. Sample space is: H,H & H,T & T,H & TT. As you can see, the probability of H,H is 1/4 and the probability of a H & T is 1/2.

How does the lack of a normal distribution influence the analytical options available to a researcher?

Most parametric and many non-parametric tests for testing the significance of hypotheses are based on the assumption of normality - or approximate normality.

How many cards must you draw from a regular deck of 52 playing cards to be sure at least 3 are from the same suit?

The first four cards could all be of different suits.

The next four cards might also all be of different suits.

This would mean that you would have two of each suit.

Then you might have to draw a ninth card to be sure of having three of the same suit.

What does it mean to say that the chances of getting a head when a coin is tossed are one-half?

It means that if the coin were tossed an infinite number of times,

half of the tosses would come up heads and half would be tails.

Why is it the heart so hard to draw?

It may be easy to draw if you use symmetry.........

What are the considerations for the choice of sample size?

Some considerations are:

  • large samples take more time and money to process
  • if the characteristic of interest is very variable then a large sample is required for accurate estimates
  • if the characteristic of interest is very rare in the population then a large sample is required to ensure that units with that characteristic are included in the sample
  • the greater the accuracy required of the estimates based on the sample, the larger the sample required.
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