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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

Probability of winning the lottery?

To calculate the odds of winning lotto where choose say 6 numbers out of 40 for example the calculation is 40X39X38X37X36X35 divided by 6X5X4X3X2X1 or about 3.8 million to 1 on any one line. If you have 45 numbers to choose from it would be 45X44X43X42X41X40/6X......etc or about 8.2 million to 1.

In an s orbital the probability of finding an electron a particular distance from the nucleus does not depend on a quantum mechanical model direction with respect to the nucleus the schrodinger e?

To the extent that I can make any sense of the question: Yes, the probability function for an s orbital is spherically symmetric and dependent on radial distance only.

What is the probability of rolling a 6 with a single roll on a dice?

one in six

1:6

six sides, one of which is a six

same odds for any of the numbers

How many queens are in a deck or cards?

There are four queens in a deck, one for each of the suits, spades, hearts, diamonds, and clubs.

What is the probability of at least one event of 20 year frequency occurring in 50 years?

The random variable has a Poisson distribution with parameter L = 1*50/20 = 2.5.

So Prob(at least one event in 50 years) = 1 - Prob(No events)

= 1 - L0e-L/0! = 1 - e-2.5 = 0.918 approx.

What is the probability of getting 3 heads and 3 tails if a fair coin is tossed 6 times?

only about 75% because very often it is not equal

The probability of 3 heads and 3 tails is 0.3125

What is the chance of drawing a number7 of cards?

The probability of drawing a seven in a standard deck of 52 cards is 4 in 52, or 1 in 13, or about 0.07692.

How many ways can 5 people sit in a row if two of them will NOT sit by each other in the row?

a.b..

a..b.

a...b

.a.b.

.a..b

..a.b

6 possible ways for two people not to sit next to each other

double that to 12 if b comes before a.

there is 1x2x3 = 6 possible for the dots on each of the above 12 combinations

so answer = 6x12 = 72

* * * * *

The correct answer is derived as follows:

The total number of ways of seating 5 people in a row is 5x4x3x2x1 = 120.

Rather than work out the number of ways in which the two people do not sit together, it is simpler to work out the number of ways in which they do sit together and subtract this from the total.

For this purpose, it is possible to treat the two people as one entity and so that gives 4*3*2*1 = 24 ways. However, this number needs to be doubled to allow for the two people to swap places: making 48 such ways.

The final answer, therefore, is 120 - 48 = 72 ways.

What is the probability of drawing an Ace and then a 7 from a 52 card deck?

The probability of drawing an ace and then a seven from a standard deck of 52 card is (4 in 52) times (4 in 51), or 16 in 2652, or 4 in 663, or about 0.006033.

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