Probability

in a card deck with only 52 cards and a 5 card hand

the probability is (52/52)(3/51)(2/50)(1/49)(48/48)=14976/311875200=3/62475

thus meaning you have a 3 out of 62475 chance of obtaining a four of a kind

Whenever Mendel performed a cross with pea plants, he carefully categorized and counted the many offspring. Every time Mendel repeated a particular cross, obtained similar results. For example, whenever Mendel crossed two plants that were hybrid for stem height (Tt), about three fourths of the resulting plants were tall and about one fourth were short. Mendel realized that the principles of probability could be used to explain the results of genetic crosses.

Total possibilities = 9x8

Uncracked possibilities = 3x2

= 6/72

= 1/12

Rolling the dice once will result in any one of the six numbers having the same probability of being up. The probability of getting a '5' = 1/6, the same as getting a '1.'

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The card numbers are used by the US Playing Card company to determine brand, size specification, and face index. They are on Jokers but are better indicated with the Ace of Spades.

808 means standard index poker size.

88 means jumbo index poker size.

Other numbers include:

404 means standard index miniature size.

48 indicating a standard index Pinochle deck. (Jokers are not in this deck)

8082 is used for the novelty Big Bicycle deck.

There is also 92, which is used to identify Bee cards.

Molecular aggregates in which the individual molecules (monomers) are arranged in a regular fashion are of particular interest because of their unique electronic and spectroscopic properties, for example J-aggregates and H-aggregates. The J-aggregate is a one-dimensional molecular arrangement in which the transition moments of individual monomers are aligned parallel to the line joining their centers (end-to-end arrangement). The H-aggregate is also a one-dimensional array of molecules in which the transition moments of individual monomers are aligned parallel to each other but perpendicular to the line joining their centers (face-to-face arrangement). The most characteristic feature of J-aggregate is that they exhibit a narrow peak (J-band) red-shifted in the absorption spectrum with respect to the monomer absorption. The absorption spectrum of the H-aggregate consists of a blue-shifted band (generally is not as narrow as the J-band) with respect to the monomer absorption. The energy shift of the absorption bands of the aggregates has been explained by exciton theory.

You have to know the concentration first. That will either be in grams per milliliter (or milligrams per milliliter), or it could be in moles per liter (molarity). If it's given in grams per milliliter, just multiply that number by 60 and multiply by 1000.

If it's given in moles per liter, than first find how many moles in 60 mL by multiplying by 0.06, and then convert moles to grams using the molar mass of caffeine (194.19 grams per mole).

See the Related Questions for how to convert moles to grams.

When Johnson broke the world record for the 200 meter dash at the Summer Olympics in Atlanta in 1996, he ran the first 100 meters in 10.12 seconds. As incredible as it may sound, he ran the second 100 meters in 9.19 seconds which, as of October 15, 2007, is .55 seconds below the world record in the 100 meter dash. Historians have compared that run with the long jump of Bob Beamon in the 1968 Summer Olympics in Mexico City where he broke the existing world record by 21 3/4 inches or .55 meters.

He had a running start for the second 100.

its likely but might not the chances of the shild not having a widows peak are 1/16 you can better know these odds if you know the parents genotype or genetic makeup.

The answer depends on what sort of dice you roll and how many.

It is 10C4 = 10!/(6!*4!) = 10*9*8*7/(4*3*2*1) = 210

1

The sample size is likely to be too small.

The probability of drawing a 10 or a diamond out of 52 cards is 16 in 52, or 4 in 13.

There are 4 tens and 13 diamonds, but one ten is also a diamond, so there are 16 cards that are a ten or a diamond.

If X has the Poisson distribution with mean l

then Pr(X = k) = e-llk/k!

Mean of Poisson = Sum over all k of [k*P(X = k)] which happens to be l.

= Sum over all k of [k*e-llk/k!]

= Sum over all k of [e-llk/(k-1)!]

= Sum over all j of [le-llj/j!] where j has been substituted for k-1

= l*Sum over all j of [e-llj/j!]

But the quantity being summed is simply the pdf of the Poisson distribution and so its sum over all possible values is 1

So Mean = l

And then Variance of Poisson = Sum over all k of [k2*P(X = k)] - l2.

= Sum over all k of [k2*e-llk/k!] - l2

Then, since k2 = k*(k-1) + k

Variance = Sum over all k of [k*(k-1)e-llk/k!] +Sum over all k of [k*e-llk/k!] - l2

= Sum over all j of [l2e-llj/j!] where j has been substituted for k-2

+ Sum over all i of [le-lli/i!] where i has been substituted for k-1 - l2

= l2*Sum over all j of [e-llj/j!] + l*Sum over all i of [e-lli/i!] - l2

And since the sums are equal to 1,

Variance = l2 + l - l2 = l

Apologies: I did the answer using the symbol for lambda but this browser changed them all back to l. I cannot change them all t o something else but I hope it is clear. At least they are distinguishable from 1!

Approximately 2%

You will only win with 2 numbers if they also have the mega ball with them. You will win $10.00.

Smaller

There is no chance for a colorblind daughter because the x-chromosome that comes from the male is normal and then it does not matter which x-chromosome comes from the female because colorblindness is a recessive gene, therefore there is no chance.

The probability is 4/52*3/51 ~= 0.0045 = 0.45%

1/52

and then if you guess again without replacing the card, the denominator lowers.

So:

3 of hearts! 1/52

(2 of clubs tossed out)

... oh dang, um, well jack of spades, 1/51..

etc.

as long as you don't guess a card that's been tossed out (in which case its 0% lol)

You want the probability of miss and miss and miss which is .67 * .67 * .67 = 0.301.

365^P5/365^5=