Probability

The answer depends on the shape of the spinner.

The answer depends on how many cards are drawn, and whether they are drawn with or without replacement. If 1 card is drawn, the probability is 0, if 50 cards are drawn (without replacement), the probability is 1.

If only two cards are drawn, at random and without replacement, the probability is (4/52)*(3/51) = 12/2652 = 0.0045

One would need more facts about the situation to be able to answer this question.

If 10% of plain M&Ms are blue and you have a sample of 20 M&Ms only two of them will be blue. If you need to have 15 blue M&Ms, then your sample size should be 150 M&Ms because 15 is 10% of 150.

There are 16 possible outcomes, each of which is equally likely. So each has a probability of 1/16

HHHH: X = H*T = 4*0 = 0

HHHT: X = H*T = 3*1 = 3

HHTH: X = H*T = 3*1 = 3

HTHH: X = H*T = 3*1 = 3

THHH: X = H*T = 3*1 = 3

HHTT: X = H*T = 2*2 = 4

HTHT: X = H*T = 2*2 = 4

HTTH: X = H*T = 2*2 = 4

THHT: X = H*T = 2*2 = 4

THTH: X = H*T = 2*2 = 4

TTHH: X = H*T = 2*2 = 4

HTTT: X = H*T = 1*3 = 3

THTT: X = H*T = 1*3 = 3

TTHT: X = H*T = 1*3 = 3

TTTH: X = H*T = 1*3 = 3

TTTT: X = H*T = 0*4 = 0

So, the probability distribution function of X is

f(X = 0) = 1/16

f(X = 1) = 4/16 = 1/4

f(X = 2) = 6/16 = 3/8

f(X = 3) = 4/16 = 1/4

f(X = 4 = 1/16

and

f(X = x) = 0 for all other x

10

The event after the first and second events but before the fourth, of course!

There are at least two situations.

Consider the situation where the population consists of a number of sub-populations (strata) such that units within a sub-population are similar to one another but there are much larger differences between units from different sub-populations. In order to ensure that the sample is representative, it may be sensible to use stratified random sampling. The sampling proportion may be a constant proportion or may even be such that the variance in each stratum is similar.

The situation may also arise if the population is widely scattered geographically. Rather than expend time and money travelling all over the place, you could employ cluster sampling. Select a number of clusters of the population and then, within each cluster, carry out a census.

0.866

short answer; it depends.

Generally, you can say the probablility of an event having a specific outcome is the number of ways in which that outcome can occur divided by the total number of ways any outcome can occur. For example, the likelihood of drawing a heart from a standard 52 card deck is 13/52 because there are 13 possible results that have the desired outcome (IE 13 heart cards) and 52 total possible outcomes (52 possible cards).

22 s and 43 w are coordinates. The coordinates reference Rio de Janeiro.

1/6 x 1/6 x 1/6 = 1/216

It is 5/32 = 0.15625

The answer depends on the shape of the spinner and the numbers on it.

The probability of an event is defined as the ratio of favourable outcomes to total outcomes. In the case of discrete distributions these will be represented by numbers, while for continuous distribution they will be measured as areas.

In either case, the first measure is non-negative and the second is positive and so the probability is greater than 0. Also, the number of favourable outcomes cannot be greater than the total so the probability must be at most 1.

Observation Learning

I understand this to mean, what is the probability of getting 4, then 5 then 1?

1/6 x 1/6 x 1/6 = 1/216

There is always an element of random error and so an exact answer is not possible.

A standard deck of playing cards consists of 4 suits: Spades, Hearts, Diamonds and Clubs. You can see them, in Word for example, by using 2660 Alt+X, 2665 Alt+X, 2666 Alt+X and 2663 Alt+X respectively. Cards sharing one of these symbols are said to be in the same suit.

Counting Aces as a face card, the answer is 0.0241

If Aces are not considered face cards, then the answer is 0.0181

1 in 2

A mathematician or a statistician.

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