Probability

two=1way

three=2ways

four=3ways

five=4ways

six=5 ways

seven=6 ways

eight=5ways

nine=4ways

ten=3 ways

eleven= 2 ways

twelve=1 way.

Seven has the most ways, so seven is the most commonly rolled number.

There are twenty six ways out of thirty six possible rolls of two dice to hit a number less than nine OR a seventy two percent probability.

tt

13/52 (if you're not playing with the two jokers. If you are then it would be 13/54)

(1, 5, 6, 6), (2, 4, 6, 6), (2, 5, 5, 6), (3, 3, 6, 6), (3, 4, 5, 6), (3, 5, 5, 5), (4, 4, 4, 6), (4, 4, 5, 5).

If you toss a coin 8 times and there are 7 heads, then there must be one tail each time.

So how many ways can we get one tail?

It can occur first, such as THHHHHHH or second HTHHHHHH etc.

There are 8 places to put the T so there are 8 ways to have 7 heads and 1 tail.

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 probability of flipping a coin 3 times and getting 3 heads is 1/2

It means that equilibrium may be attained at widely separated values.

The Normal distribution is a probability distribution of the exponential family. It is a symmetric distribution which is defined by just two parameters: its mean and variance (or standard deviation. It is one of the most commonly occurring distributions for continuous variables. Also, under suitable conditions, other distributions can be approximated by the Normal. Unfortunately, these approximations are often used even if the required conditions are not met!

It means that the data are distributed according to a probability distribution function known as the normal distribution. This site is useless for showing most mathematical functions but you can Google "normal distribution" to get more details.

There are 19,958,400.

Prob(Sum is not divisible by 3) = 24/36 = 2/3

There are no sure and positive outcomes. Group therapy will help some people and fail with others.

It means that there is a probability or chance of 0.05 or 1 in 20 of observing the relevant event.

It is dependent.

1/64

There is a chance that it might be.

60

1.00

A dependent event is one that relies on something else to happen.

For instance with a mouse trap the trap closing "depends" on the trigger being activated.

360

Pr(Windy given not Sunny) = Pr(Windy and not Sunny)/Pr(not Sunny)

= 0.2/(1 - 0.3) = 0.2/0.7 which rounds to D 29%

4.55% falls outside the mean at 2 standard deviation