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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

If there are 14 white marbles and 28 red marbles what is the probability that you would pick a white marble?

14/42. You have to add the amount of marbles and then put the probabilityof answers you're looking for.

Ex:

14 white marbles

28 red marbles

14+28=42

?/42

your looking for the probability of white marbles, so you put in the amount of white marbles on the fraction.

=14/42

What is your initial velocity if you traveled 25 miles in 2 minutes and your final velocity is 0 mile per hour?

If you traveled 25 miles in 2 minutes, your average speed was 25 miles per 2 minutes or 750 miles per hour. If your rate of deceleration was constant, your initial speed was two times 750 miles per hour or 1500 mph.

I do not have enough information to determine your initial velocity because I don't know what direction you were going, and velocity is speed with direction.

What happens if you estamate 23975?

Tenths: 23980

Hundredths: 24000

Thousandths: 24000

Ten Thousandths: 20000

How do the width and height of a normal distribution curve?

By standard practice, the normal distribution curve should be normalized so that the area under the curve is 1. This results in a height, at the mean, of about 0.4, i.e. the probability of a sample value being equal to the mean is 40 percent.

The width of the normal distribution curve is infinite, as the tails are asymptotic to the X axis. It is easier to understand that the +/- one sigma area is 68.2 percent, the +/- two sigma area is 95.4 percent, and the +/- three sigma area is 99.6 percent.

How do you focus efforts on certain activities to make the best use of resources?

You apply econometric analysis to the range of possible activities. Economics is the study of allocation of [limited] resources so as to maximise benefit.

What is the probability that any two people in a random group of 30 have the same birthday that is the same month and date?

It is approaching unity that two in a random group of 30 people would have the same birthday. (Month and date)

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P(2 people share bd in 30) ≈ 38.0%

Using the following expression* that doesn't consider February 29 of a leap year but

gives good estimate;

P(2 people and only 2 people share a birthday, month and date, in a group of n people) = nC2 (1/365) Π1n-1(1 - (i-1)/365)

nCr = n!/(r!(n-r)!)

for n = 30, r = 2,

30C2 = 435

P(2 people share bd in 30) = 435(1/365)(1)(1-1/365)(1-2/365)∙∙∙

∙∙∙(1-27/375)(1-28/365) = 0.380215577...

P(2 people share bd in 30) ≈ 38.0%

*[For an expression that considers leap year see question "What is the probability that

in a room of 8 people 2 have the same birthday ?"]

If a gambler rolls two diceand gets a sum of 10 he wins 10 dollars and if he gets a sum of 3 he wins 20 dollars The cost to play is 5 dollars What is the expected value of the game?

P(rolls a ten)=3/36=1/12

P(rolls a three)=2/36=1/18

[I am going to assume that if he rolls a ten or three, he also gets his five dollars back, in addition to the winnings.]

Expected value=(1/12)*10+(1/18)*20-(31/36)*5=-85/36, or approximately -2.36

If he doesn't get his five dollars back when he wins,

Expected value=(1/12)*10+(1/18)*20-5=-110/36, or approximately -3.055

[I actually just had this on my statistics final.

I got this one wrong still don't know the answer, but the answer you have isn't one of the possible answers I had.... Maybe -2.78?]

How many different ways can you arrange the letters in a six letter word?

If all the letters are unique in the set, there are 6 choices for the first letter, 5 for the second letter, 4 for the third letter, etc. This results in 6 X 5 X 4 X 3 X 2 = 720 arrangements. If some of the six letters are duplicated, there will be fewer distinct arrangements.

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