Probability

The answer depends on whether or not the events are independent, whether or not the probabilities are the same for each event etc. Without that information, there cannot be an answer.

If you fall from any given height, whether or not you get hurt will depend on a large number of factors: what you fall on, how you fall, whether or not there was something that broke your fall on the way down and so forth.

The range of vales of the event is the outcome space.

If you roll the die often enough, the event is a certainty and so the probability is 1.

If you consider only the first 5 rolls, the answer is (1/6)5 = 1/7776 = 0.000129 approx.

There are 720.

This is the same as the probability of choosing either a red of a blue marble.

There are 5+4 out of 15 ways of doing this. The probability is therefore 9/15 = 3/5.

1 in 2

A mathematician or a statistician.

4: the two m and o can be swapped without affecting the spelling.

Well there are six possibilities, the four jacks and the two black threes. This gives us a fraction of 6/52 which is a percentage of 11.54%

It is: 1 in 3

1/6 x 1/6 = 1/36

21/36 = 7/12

1-365/[(365-6)*365^6] = 1 Is this O.K ?

It represents the number of favourable outcomes divided by the highest common factor of the number of favourable outcomes and the total number of outcomes.

By definition, the 1st 6-tile is the point below which 1/6 of the population falls (irrespective of which distribution is involved). The 2nd 6-tile is the point below which 2/6 of the population falls.

This is 100 * 1/3 ~ 33.3% of the population.

The power of a test is 1 minus the probability of a Type II error.

You could buy (4+1)*(3+1) = 5*4 = 20 combinations. This includes the combination of buying none.

Assuming that all the cedar trees are the same and that the three apple trees are the same, and it doesn't matter which of the apple trees you purchase, then you have the following options: CCCCAAA, CCCCAA, CCCCA, CCCC, CCCAAA, CCCAA, CCCA, CCC, CCAAA, CCAA, CCA, CC, CAAA, CAA, CA, C, AAA, AA or A. This is 19 possibilities.

Because the problem says that you buy trees, the null set (i.e., not buying anyting) is not as option.

The probability of flipping Heads on a coin is 1 - a certainty - if the coin is flipped often enough.

On a single toss of a fair coin the probability is 1/2.

A single roll of a fair number cube: 1/2

A single toss of a fair coin: 1/2

Both events: 1/4

The number of permutations of the letters of the word depends upon the number of letters in the word and the number of repeated letters.

Since there are nine letters, if there were no repetitions, the number of ways to rearrange these letters would be 9! or 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1. But don't do the multiplication just yet.

To account for the repeated letters, we need to divide by 3! (for the 3 Ns) by 2! (for the 2Es) and by another 2! (for the 2 Ss).

This gives a final answer of 15,120 permutations of these letters.

-- 8 possibilities if the coins are different colors.

-- Only 4 possibilities if you can't tell the coins apart.

The probability is 1. I have flipped a coin a lot more than 7 times.