Probability

A parameter describes a population. A statistic describes a sample.

If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.

There are 4 Kings in a standard pack of 52 cards.

If 1 King has previously been drawn this now leaves 3 kings out of a total of 51 remaining cards. The probability of now drawing a King is therefore 3/51 which simplifies to 1/17.

Note: this is the probability concerning the 2nd draw only.

1/100

There are eight different letters in 'mathematics' - a, c, e, h, i, m, s and t.

Since there are 26 letters in the alphabet, the chance of a randomly chosen one being a letter that's in mathematics is 8/26, or 4/13.

The probability of rolling a odd number on a standard die is 3 in 6, or 1 in 2, or 0.5.
You don't say with what, so I assume with a standard six sided die. The probability of rolling an odd number with a standard six sided die is 3 in 6, or 1 in 2, or 0.5.

2600

There are 6 sides on a die, so the denominator should be 6. The number 3 appears on the dice once, so the fraction probability should be 1/6.

There are a total of six outcomes if you roll one die.

The probability of rolling a composite number on a 6 sided die, numbered 1, 2, 3, 4, 5, and 6, is 1 in 3.

There are two composite numbers on the die, 4 and 6. The others are prime, 2, 3, and 5, or unity, 1, so there are 2 possible outcomes in an possible result set of 6, hence the probability is 2 in 6, or 1 in 3.

There are 20 ways to choose the first sample, which leaves 19 ways for the second one, and 18 for the third one. So (apparently) there are 20 x 19 x 18 ways to choose a sample of 3 items, BUT, since the order of choosing a particular set of 3 doesn't matter, we need to divide by 3 x 2 x 1; so the final calculation is (20 x 19 x 18) divided by (3 x 2 x 1). Cancelling by the 3 and the 2 we have 10 x 19 x 6 = 10 x 114 = 1140

The probability depends on the availability of marbles of those colours to the person making up the bag.

independent

See related link. Other people may not view the same events as important.

Yes.

63=6*6*6=216

Not necessarily. It might mean that the experiment has a highly stable outcome. You need to evaluate if that is true or if the experiment is flawed. It comes down to theoretical expectations versus experimental outcomes - you should know a priori (before the fact) what to expect, so you can know if the results are good.

For instance...

If you were measuring the radioactivity of a sample with a relatively low count rate using a detector that recorded counts in each second, you would expect a poissen distribution.

If you were measuring the same sample with a detector that counted for 1 minute, you would expect a more gaussian distribution.

If, on the other hand, you were measuring the wavelength of a red laser, you would expect that every single observation would give you the same results, within an extremely tight distribution.

The standard deviation.z-score of a value=(that value minus the mean)/(standard deviation)

Systematic sampling

Probability of girl, assumed to be 0.5. Therefore, probability of 5 girls is 0.5^5 or 0.03125.

yes

There is one way to roll a sum of 12.

There are 36 different outcomes from rolling a pair of dice.

Therefore, the probability is 1/36 ~= 0.0278 = 2.78%

If B is between P and Q, then:

P<B<Q

You draw a perpendicular at the end of a line segment. You then bisect the right angle formed between the original line and the perpendicular. The resulting angle will be 45 degrees.

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