Probability

It is a probability distribution where when all of the values of a random variable occur with equal probability.

Say X is the random variable, such as what number shows up when we roll a die.

There are 6 possible outcomes, each with a 1/6 probability of showing up.

If we create a probability distribution where X= 1,2,3,4,5, or 6, we note

P(X=k)=1/k where k is any number between 1 and 6 in this case.

The graph will be a rectangle.

31

what are the odds in favor of drawing a diamond from an ordinary deck

Basically, this is the same as finding the number of distinct ways of arranging seven 1s and 3 0s. That is (10!/7!3!) = (10*9*8)/(3*2*1) = 120.

There are 120 bit strings of length 10 with exactly three 0s.

No; because probability can never be less than zero.

Yes.

1/26 under the assumption that one is using a standard 52 card deck with no jokers. 1/27 if the jokers are included.

The study of ergonomics as a way to reduce human error began in the military during the Korean War.

1/52, or One over Fifty-Two.

The odds are so because there are fifty-two cards in a deck, and there is only one Queen of Spades.

The chances of you picking a Queen of Spades is One in Fifty-Two tries.

If you are using jokers, 1/54, because there are 2 extra.

12.5%

The probability of a result you want is

(the total number of results that would satisfy you) divided by (the total number of all possible results).

1 out of 6

6 to 108

It depends what you consider favorable.

There are 6 possible outcomes of a single roll of a 6-sided die.

The one-tailed z-value is:

P(Z < z) = 0.9693 => z = 1.8706

You can use the z test for two proportions.

The link below will do this test for you.

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"A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Méré, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well-established gambling rule led de Méré to believe that betting on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite.

Assuming you're using 6-sided dice, The probability of rolling less than 4 on one die is 1/2. To roll 3 dice and get less than 4 on 2 (and only 2) of them is 3/8.

The Poisson distribution with parameter np will be a good approximation for the binomial distribution with parameters n and p when n is large and p is small. For more details See related link below

The expected outcome is the sum of (each possible occurrence times the probability of that occurrence).

For example, the expected outcome of rolling one die is:

1 * 1/6 + 2 * 1/6 + 3 * 1/6 + 4 * 1/6 + 5 * 1/6 + 6 * 1/6 = 3.5.

the word great has 5 different letters..

so at 1st place 5 different letters can exist, at 2nd, left 4 letters can exist, at 3rd.. 3 left letters, at 4th, 2 left letters and 5th ..1 left letter..

so for permutation... we do possible options at 1st place X possible options at 2nd place ... and so on till X possible options at 5th place.

= 5 X 4 X 3 X 2 X 1

=20 X 6

= 120

so the word great has 120 possible permutations.