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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
How many sums are there with two dice?
If you roll two dice and add the numbers together, you might get 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, so there are eleven possibilities total. One is not included in this list because that would mean the first dice would roll a one and the second dice would roll a...zero? That's impossible!
7/128, or about 5.5%
The student has a 1/2 probability of getting each question correct. The probability that he passes is the probability that he gets 10 correct+probability that he gets 9 correct+probability that he gets 8 correct:
P(passes)=P(10 right)+P(9 right)+P(8 right)=[(1/2)^10]+[(1/2)^10]*10+[(1/2)^10]*Combinations(10,2)=[(1/2)^10](1+10+45)=56/1024=7/128.
What is a possible outcome for a protostar that does no have enough material?
A brown dwarf.
A brown dwarf.
A brown dwarf.
A brown dwarf.
List ways to express mathematical probability in genetics?
Probability formulas can be used to predict the probabilities that specific alleles will be passed on to offspring.
If we are thinking of getting a '6', here are the odds.
Wth one dice, its 1 in 6.
So,with two dice its 1 in 216
with three dice its 1 in 7776
with four dice its 1 in 279936
with five dice its a huge 1 in 10077696
1/16
These are four independent events each with a 1/2 probability. The probability that all four occur (penny and nickels heads and dime and quarter tails) is: 1/2*1/2*1/2*1/2=(1/2)4=1/16.
When you roll a fair 6 sided die it is harder to roll a six than a four?
When you roll a fair 6 sided die it is no harder to roll a six than a four. Each possible outcome has the same probability. That is the definition of "fair".
Isotherm
Consider a surface:
Definition:q0, q1, ..., qn = Surface area (cm-2) covered by 0, 1, ..., n layers of adsorbed molecules.
At Equilibrium:q0 must remain constant. . Rate of Evaporation Rate of Condensation . . = from First Layer onto Bare Surface
Similarly, at equilibrium q1 must remain constant. . Rate of Condensation Rate of Condensation . . on the Bare Surface on the 1st Layer + = + Rate of Evaporation Rate of Evaporation from the second layer from the second layer . . . k1Pq0 + k-2q2 = k2Pq1 + k-1q1
Substituting into (I) gives
k-2q2 = k2Pq1
Extending this argument to other layers,
Definitions:
Total surface area of the catalyst,
Total volume of gas adsorbed on surface
where v0 is the volume of gas adsorbed on one square centimeter of surface when it is covered with a complete layer. . . .
where vm is the volume of gas adsorbed when the entire surface is covered with a complete monolayer.
From (I),
If we assume that the properties of the 1st, 2nd, ... layers are equivalent, then,
Similarly,q3 =xq2 =x2q1
Generally,qi =xqi-1 =xi-1q1 =xi-1yq0 =cxiq0 {c=x/y}
Substituting into (V),
Now,
Also, . . .
At saturation pressure of gas P0, an infinite number of adsorbate layers must build up on the surface. From equation VII, for this to be possible,
must be infinite. This means that at P0, x must equal 1. . . . g = P0(From definition of x) . . . x = P/P0
Substituting into VII, we arrive at the recognized form of the BET isotherm,
This can be rearranged to give,
What are Advantages and disadvantages in multistage sampling?
Advantages are:
1. Fewer investigators are needed
2. It is not so costly to obtain a sample
Disadvantages are:
1. There is the possibility of bias if, for example, only if a small number of regions are selected
2.The method is not truly random as once the final sampling areas have been selected the rest of the population cannot be in the sample.
If the population is heterogeneous, the areas chosen should reflect the full range of the diversity. Otherwise, choosing some areas and excluding others (even if it is done randomly) will result in a biased sample.
If you toss a coin 5 times how many outcomes are there?
For a coin toss, there are 2 possible outcomes (heads or tails). For five tosses, therefore, there are 25 possible outcomes (25 = 32). However, this assumes that order is important (i.e. that HtttH is different to tHtHt). If you don't care what order the heads or tails fall in, there are only 6 outcomes.
What is the probability of prime numbers being chosen randomly from the number 1-49?
15/49
Explanation
There are 15 prime numbers between 1 and 49 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47). If you randomly choose one natural number from the 49 numbers between 1 and 49 inclusive, there is a 15/49 probability that it will be prime.
If you flip a coin 5 times what is the probability that the results are all heads or all tails?
The probability of getting all heads or all tails in 5 flips of a coin is 1 in 16.
The probability of getting a head or a tail on the first flip is 1 in 1. The probability of each of the following coins matching the first coin is 1 in 2. Simply multiply the five probabilities (1 in 1) (1 in 2) (1 in 2) (1 in 2) (1 in 2) and you get 1 in 16.
It is true that the probability of getting all heads is 1 in 32, and the probability of getting all tails is also 1 in 32. Since the question asked the probability of both cases (all heads or all tails), the answer is 1 in 16.
A coin is fipped and a number cube is rolled so what is the sample space of the experiment?
The sample space of a coin and a die is [H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6].
Are the questions on the AMC 10 multiple choice or short answer?
The American Mathematics Competition 10 (AMC 10) is made up of 25 multiple choice questions (A through E). All questions are worth 6 points if correct, 0 if incorrect, and from 1.5 to 2.5 points if blank depending on the year. Recently the contest has moved toward 1.5 points for a blank answer.
The probability when you roll two dice that you roll an odd number on the first die and a 1 on the second die is 1 in 12.
The two die are sequentially unrelated, so you can consider them separately. The probability of rolling an odd number is 3 in 6, or 1 in 2. The probability of rolling a 1 is 1 in 6. Multiply the two probabilities together and you get 3 in 36, or 1 in 12.
58=390625
There are five choices for each of the questions. To find the total number of ways to answer multiply 5 for each of the eight questions.
The minimum number of cards that must be dealt, from an arbitrarily shuffled deck of 52 cards, to guarantee that three cards are from some same suit is 9.
The basis for 9 is that the first four cards could be from four different suits, the next four cards could be from four different suits, and the ninth card is guaranteed to match the suit of two of the previously dealt cards. The minimum number, without the guarantee, is 3, but the probability of that is only 0.052, or about 1 in 20.
If it is a fair coin, the probability is exactly 50%. The coin has no memory of what it did in the last flip. ■
Ace combat 4 how do you eject?
To eject just press L1 R1 L2 and R2 all at the same time. Hope this helps.
decreases
Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
