Probability

A probability event that is impossible is one that will not happen, i.e. its probability is zero.

The probability of rolling a particular face in a 12 sided die is 1 in 12, or about 0.0833.

there is no end to numbers so the probability is very high

The probability of tossing two heads in two coins is 0.25.

The probability of getting two tails when tossing a coin is zero, because the coin can only have one result.

If, one the other hand, you toss the coin twice, then the probability of getting two tails is 0.25, i.e. the probability of one tail, 0.5, squared.

the probability of tossing a coin and it landing on head is a 1 in 2 chance the probability of rolling a 5 on a dice is a 1 in 6 chance

Theoretical probability.

all probabilities smaller than the given probability ("at most")

all probabilities larger than the given probability ("at least")

It depends on how many positions are on the spinner, and on how many of those positions are fours.

Assuming a full, regular deck, no jokers? There are 52 cards in such a deck, 26 red and 26 black, making the odds of drawing a red card exactly 1 in 2.

4/12

Marble is not transparent (can't see an image through it). Thinly cut marble is translucent (can see light through it).

It means that the probability density function is symmetric about 0.

It will not. For the interval (x, x+dx) it may well give a non-zero probability.

With a continuous distribution, the probability of any particular value is always 0. What the probability density function gives is the probability that the variable is NEAR the selected value.

Z scores are used for standardized testing done by most school districts.

It is the most common way of standardizing data. IQ scores can be standardized using z scores. The mean is 100 and the standard deviation is 15.

You use the t score when the sample is small, <30 often. Many behavior ratings use t scores.

The null hypothesis could be that the 40 students are a sample from the same (or similar) population.

5 cards out of 52 may be drawn in 52C5 = 2 598 960 ways.

2 aces out of 4 may be drawn in 4C2 = 6 ways.

3 non-aces out of 48 non-aces may be drawn in 48C3 = 17 296 ways

P( 2 aces ) = (4C2)(48C3) / (52C5) = (6)(17 296)/( 2 598 960)

= 0.0399

1 out of 555555

We know there are 10! (ten factorial) permutations (that's about 3,628,800 permutations); however, we know that number includes repeated permutations, as there are 3 s', 3 t's and 2 i's. So we have to divide by the number of ways these can be written as individual permutations (if they were considered as unique elements), which are 3! (= 6), 3! and 2! (= 2) respectively.

So our final calculation would be 3628800 / (6 * 6 * 2) = 50400 unique permutations.

3

(1/2)^3 = 1/8

In general it is like this (p/n)^t. Where n is the number of equally possible outcomes (2 since you can get heads or tails), p is the number of desired outcomes (1 since you only are concerned with heads), and t is the number of trials (3 in this case).

One caveat to this is that it does not factor in initial conditions. Although very slight you have a better chance of getting heads when the coin is flipped from a position where heads is up. You have less chance of getting heads when the coin is flipped from the tails-up position. This effect is decreased the more the coin flips before landing.

If you assume that the Ace is high, then the odds of drawing a card higher than a nine is a standard deck of 52 cards is 20 in 52, or 5 in 13, or about 0.3846.

If you assume that the Ace is low, then the odds of drawing a card higher than a nine is a standard deck of 52 cards is 16 in 52, or 4 in 13, or about 0.3077.

There is no possibility that a male will inherit and X-linked recessive allele from his father because for a male child the father only contributes the Y chromosome to his son (of the XY pair he has). If the fater's X chromosome has a recessive allele then it is 100% certain that he will pas this on to all his daughters.

24