Probability

Rethink the question as "How many ways can the letters of MISSISSIPI (one P) be arranged?" The (initial) answer is that this is the number of permutations of 10 things taken 10 at a time, because every time you choose a P, you simply write down two P's. That is 10 factorial, which is 3,628,800. However, since there are still multiple letters (four S's, and four I's), you need to divide by 24 twice in order to see how many distinct permutations there are. That is 3,628,800 / 16 / 16, or 14,175.

Strictly speaking, there are no cons because they are defined for discrete variables only. The only con that I could think of is the difficulty evaluating the moments and other probabilities for some discrete distributions such as the negative binomial.

z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.

what is the z score for 0.75

One quarter of the pack are CLUB cards. Three quarters of the pack are NOT CLUB cards.

So the chance (probability) of picking a CLUB card is 1 out of 4 = 0.25

The chance (probability) of picking a NOT CLUB card is 3 out of 4 = 0.75

Adding the various probabilities the answer must always be 1.0, which is true here.

If the probability of something happening is 1.0, that means the probability is "certainty". It is bound to happen.

In a standard normal distribution curve, one half of the area is .5 (or 50%). 0 is the middle value of the z-score. So, for an area of .7704, z must be negative. Also, the area from 0 to z (which is negative) must be equal to .2704. From the normal probability table, this value is -0.74

Therefore, the z-score for the area equals 0.7704 is -0.74

The set of possible outcomes is the set of different ways in which an event might or might not happen. Take a very simple example: If you roll a dice you will roll a 6 or a 5 or a 4 or a 3 or a 2 or a 1. So there are 6 different possible outcomes, all of which are equally probable.

If you roll 2 dice at the same time the possible total scores are are from 2 ( a 1 and a 1) to 12 (a 6 and a 6), so there are 11 possible outcomes, but not all equally probable.

Two events are mutually exclusive if they both cannot occur together. For example, if you toss a coin , let A represent a head showing up and B represent a tail showing up. These two events are mutually exclusive. You can only have a tail or head.

To explain an independent event, pick a card from a deck of 52. The probability that it is a king is 4/52. If you put the card back and draw again, the probability is still 4/52. The second draw is independent of the first draw. If you draw another card without putting it back, its probability changes to 3/51. It becomes a dependent event.

In short, a mutually exclusive event is not an independent event.

Rolling 2 dice together can produce total scores from 2 (a 1 and a 1) to 12 a (6 and a 6) but there not all equally probable. You would score 6 with 1 + 5 or 5 + 1 or 2 + 4 or 4 + 2 or 3 + 3.

Because there are 6 numbers on No. 1 dice and 6 numbers on No. 2 dice there are 6 x 6 = 36 ways of scoring.

From the above you can see that your 5 possibilities out of 36 means that the probability is 5/36 = 0.138888(recurring decimal) = 13.89% correct to 2 decimal places.

There is only one card which has 10 hearts upon it, and that is the 10 of hearts. Similarly there is only one two of clubs in a 52 pack.

Samplig frame is the source material from which the sample is drawn. If you have a 'list' of names of all inviduals from which you could draw a sample, the list is a sampling frame.

A samplig unit is the sample being chosen.

There are 15,000 milliliters in 15 liters.

standard normal is for a lot of data, a t distribution is more appropriate for smaller samples, extrapolating to a larger set.

There are 65 = 7776 outcomes.

A square, rhombus and a kite

There are 6!/2! = 360 ways.

The odds against drawing a six of clubs in a standard deck of 52 cards is 51 in 52, or about 0.9808.

The laws of probability predict what is likely to occur, not necessarily what will occur.

Total numbers on the cube = 6

Numbers less than 5 = 4

Probability = 4/6 = 2/3 = 662/3 %

The following is the answer:

Coeff of Variation = Mean/SD

The probability is 10/50 = 1/5.

It depends on how many positions the spinner has, and on how many of them are a 5. The question, as stated, is incomplete and cannot be answered. Please restate the question.

if you flip a coin once, the chance it will be heads is 50%