Probability

directed numbers are used for counting, measuring, adding, subtracting, dividing and multiplying. hope this helps which it probably wont :)

According to the links, Karl Pearson was first to formally introduce the gamma distribution. However, the symbol gamma for the gamma function, as a part of calculus, originated far earlier, by Legrenge (1752 to 1853). The beta and gamma functions are related. Please review the related links, particularly the second one from Wikipedia.

55 x 55 = 3025

1/6 because there are six sides to a dice and we already know the coin landed tails up so that takes that equation out of the picture. otherwise we would be left with figuring the probability of the coin and the dice, but since the question tells us that the coin landed tails up the answer will then be 1/6

I haven't heard of a component with regards to statistics. If, by chance, you are referring to the complement, it is the probability that the event does not occur. In this case, the complement would be 0.58.

The only way to get a 12 is to get two sixes. The chance of rolling a six is 1/6 and chance of rolling two sixes is 1/36 or about 2.78%

There are 2 red jacks, so 2/52 or about .038%

#7

There are 180 different arrangements, you may punch in 6! to your calculator and get 720 and think this is right but you have to take into account that "d" and "o" and doubled, so, the arrangements will give you a different answer.

6*5*4*3*2*1/4= 180

180 arrangements. :)

1 in 4. Because there are 4 suits of cards.

If five cards are drawn from a deck of cards without replacement, what is the probability that at least one of the cards is a heart?

The answer is 1 in 1000.
Rolling a 4 on a ten sided die is a 1 in 10 shot.
Rolling threes 4's is 1/10 x 1/10 x 1/10 which equals 1/1000.

1/2 x 1/2 x 1/2 = 1/8 or 0.125 also 12.5%

This is a conditional probability, given the card is red, what is the chance it is a heart. Since there are 2 red hearts, the probability if 1/2

There are 16 marbles total and 7 green ones, so the probability is 7/16.

there are 3 types of conditional probability:

1. the indicate: if antecedent happens, then evidence manifests itself

example -> when tossing a coin, if it lands on tails, then you win the game

2. the subjunctive: if antecedent would happen, then evidence would manifest itself

example -> when a coin was tossed, if it would have landed on tails, i would have won the game

it is recommended for optimal bayesian inferences that your a priori distribution is indicative. If not, you could be dealing with inproper, uninformative, or hyper priors, which make decision-making and posterior determination more complex, if even possible.

Posterior distributions could very well be subjunctive. Suppose i have won the game, i could have tossed tails, but i could also have tossed heads.

50/50

It can be thought of as a generalization of the Chi-square distribution. See the link to a related WikiAnswer question below.

3/8

P(A given B')=[P(A)-P(AnB)]/[1-P(B)].

In words: Probability of A given B compliment is equal to the Probability of A minus the Probability of A intersect B, divided by 1 minus the probability of B.

2

p(a) = 1/3, p(b) = 1/2, p(a and b) = p(a)*p(b) = 1/6

From a probability perspective fair means equal probability.

2:7

edit:

That makes the assumption that:

-birth isn't induced for various reasons - people tend to try for induced births more on weekends so that it doesn't interfere with the work week

-the ratio of people born on any given day of the week is 1:1:1:1:1:1:1