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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
What is the probability you roll a number cube twice and get an even number but not a 2?
The probability of getting an even number on both dice is (2/6) * (2/6) = (4/36) = 1/9.
The probability when rolling two dice of getting one even number but not a "2" is 10/36, which is 5/18.
How do you remove a rusted bolt?
There are four simple steps to try initially:
1) Clean up the seized fastener... use a combination of degreasers, detergents, abrasives and wire brushes. This sets things up for the next step...
2) Search for the term "penetrating lubricant". These are specially formulated to squeeze into the small spaces in fastener threads. Use the lubricant liberally. Use wire brushes to work it in, further cleansing the area.
3) Try to rock the fastener in both directions... particularly effective if it starts to come undone then jams. Add more lube as you go... it should rock a little further each time until it frees up. if not...
4) If seized absolutely solid try a freeze and release spray... very effective and much safer than heat around delicate electrics, heater hoses, brake lines etc.
How many different ways can you arrange 15 objects into 3?
It depends on whether they are being arranged in a line or a circular pattern.
In a line: 15*14*13 = 2730 ways.
In a circular pattern : ABC, BCA and CAB will be the same pattern, only rotated. So the answer is 15*14*13/3 = 910 ways.
What is eqivalent to 3 over 8?
As a decimal: 0.375
Or, treating this as a rational number: 6/16, 12/32, 9/24, ...
What is the probability of having exactly 8 boys in 10 births?
For each birth, you have two choices - either a boy or a girl. Then, the probability for a certain birth to obtain a choice is ½.
Using Binomial Theorem, we have (10 choose 8)(½)8(½)² = 45/1024.
How many outcomes do you get from rolling 3 coins?
23 or 8 outcomes. In any experiment with two outcomes, if you do the experiment n times there are 2n outcomes.
This about each time you roll the coin have two possible outcomes, H or T.
So if you roll it 2 times, you have 4 possible outcomes. HH, HT, TH or TT.
Do it one more time and you have 8 outcomes.
HHH, HHT, HTH, THH
TTT TTH THT HTT
Notice there are
1 outcome with 3 heads, 1 with 3 tails
3 with two heads
3 with two tails
This pattern follow the binomial theorem.
The coefficients of the binomial (H+T)3
are 1 3 3 1. The same numbers as we have above!
How many outcomes are there for a 6-sided dice and then spinning a 10-part spinner?
You multiply the possibilities so 6 possibilities of the dice and the 10 possibilities of the spinner so in total there are 60 possible outcomes for this situation.
How many 3-digit numbers can be formed using 5 6 7 and 8 if the digits can be repeated?
Each of the 3 digits in a number can be any one of the four allowed.
Total number of possibilities = (4 x 4 x 4) = 64numbers.
What are the differences between a platykurtic a mesokurtic and a leptokurtic distribution?
The kurtosis of a distribution is defined as the fourth central moment divided by the square of the second central moment. Unfortunately, this browser converts Greek characters to the Roman alphabet so I cannot use standard forms of equations but:
Suppose that for a random variable X, E(X) = m (mu)
and E[(X - E(X))2] = V = s2 (sigma-squared)
then
Kurtosis = E[(X - E(X))4]/s4.
Excess Kurtosis is then Kurtosis - 3.
If excess kurtosis < 0 the distribution is platykurtic. They have a peak that is lower than the Normal: the peak is flat and broad. The tails of the distribution are narrow. Uniform distributions are platykurtic.
A mesokurtic distibution has excess kurtosis = 0. The Gaussian (Normal) distribution - whatever its parameters - is mesokurtic. The binomial with probability of success close to 1/2 is also considered to be mesokurtic.
If excess kurtosis is > 0 the distribution is leptokurtic. Leptokurtic distributions have a high and narrow peak. A good example is the Student's t distribution.
Explain the function of flexors and in extensors?
these muscle groups either extend a joint, extensors) or contract the joint (flexors).
triceps extend the elbow joint, biceps bend the elbow joint.
What does it mean if a guy doesnt laugh when something embarrassing happens to you?
He doesn't think it is very funny.
P(Rain) = 0.4
P(No Rain) = 0.6
P(Rain on 3 out of 5 days) = 5C3x(0.6)^2x(0.4)^3 = 0.2304
P(Rain on 4 out of 5 days) = 5C4x(0.6)^1x(0.4)^4 = 0.0768
So P(Rain 3 or 4 out of 5 days) = 0.2304 + 0.0768 = 0.3072
What disadvantage are there of the mean deviations?
The mean deviation of a set of observations is always zero and so conveys no information whatsoever!
If two dice are rolled one at a time what is the probability of getting a 1 followed by a 2?
there are 36 possible combinations in two single die tosses. The odds of any one combination is then 1:36
When you ask someone for a number between one and ten why do they always say seven?
For it is a very magic number which has many kinds of meanings.
How many rolls are needed to have half the 120 dice remaining?
It depends on why the other half are disappearing!
