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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 different ways can you arrange the letters of the word awesome?

The word awesome has 7 letters where the letter eisrepeatedtwice. So there are 7!/2! = 7*6*5*4*3 = 2520 different ways.

Can you compute for mean absolute deviation with only 2 numbers?

Yes, it is 0.5*abs(a-b), where "abs" represents the absolute function: that is, a-b or b-a, whichever is greater.

How many ways are there of selecting a black card in a deck?

There are 26 different ways of selecting a black card from a standard deck of 52 cards.

How does one calculate factorials in probability on a TI 83 84 calculator?

Example: Calculate 6 factorial...

On the home screen [Clear]

Press [6] [Math] and the left arrow key - this selects the PRB menu

Press [4] for !

Press [Enter]

The answer, 720, is displayed.

What is the probability in rolling a prime and odd number?

First Answer:

With one six-sided die, the odds are one in two (right). With two dice, the odds are five in twelve (this is wrong).

Second Answer:

Broken down the following can be seen:

Number, Is odd?, Prime composition, Is prime?

1, Yes, 1^1, Yes

2, No, 2^1, Yes

3, Yes, 3^1, Yes

4, No, 2^2, No

5, Yes, 5^1, Yes

6, No, 3^1*2^1, No

Full disclosure however, the arguments that 1 and 2 are prime numbers are... well, debated. We'll just presume they are to simplify things (the arguments are rather complex compared to such a simple question; honestly though, I'm of the camp that believes 1 and 2 are not prime numbers, which makes the answer 2/6 for a single die).

So, the numbers that are both prime and odd are 1, 3, and 5. Really on a six sided dice you're just asking if what the probability that a number rolled is ODD will be. If this were a 16-sided die, the answer would simply follow the same logic, but be of a slightly different in nature.

The probability an odd number would be rolled is 1/2 for a single die (3/6). The probability that only one odd number would be rolled between two die is 1/2 * 1/2 (1/4). The probability that an odd number would be rolled but the other would be even (or visa versa) is still 1/2 * 1/2 (or 1/4). The probability that both are odd, or both are even is... again, 1/2 * 1/2 (or, again, 1/4). Lastly (and to answer your question), the probability that an odd number occurred at all when rolling two dice is the inverse of the probability that an odd number did not occur, which is 1 - (1/2 * 1/2) or 3/4, or 75%. If you think about it all possible combinations have been represented here. Take any given probability conjecture such as the probability that the first is odd and the second is even, because both possibilities are independently 1/2, the complement is likewise 1/2 and it makes life very, very simple when computing this.

What is a random vector?

A vector may be thought of as a magnitude or size (such as speed) and a direction. So a moving car may be represented by a vector that gives the car's speed and direction.

If the magnitude and direction of a vector are chosen from populations of values in some way that makes them unpredictable-or random in other words-then that vector can be said to be random.

If there's a bag with 8 marbles 4 one color and the remaining 4 another what is the probability of getting alternating colors?

The first one can be anything.

The next has to be 4/7, then 3/6, 3/5, 2/4, 2/3, 1/2

Hence the probability is (4 x 3 x 3 x 2 x 2)/(7 x 6 x 5 x 4 x 3 x 2)

= 6/210

=1/35

What is the probability of 1 to 50 at random selecting numers with 4 in the 10 place?

The answer depends on how many numbers you select!

The answer depends on how many numbers you select!

The answer depends on how many numbers you select!

The answer depends on how many numbers you select!

What are the odds that when you roll two dice the sum will be greater then 5?

When you roll two dice the odds the sum will be greater than 5 are 13 out of 18, or

the probability is 13/18 = 0.72222... ≈ 72.2%.

The number of permutations of the numbers of the two dice which sum is greater

than 5 is 26:

(1,5), (1,6), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,2), (4,3), (4,4), (4,5),

(4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

The probability for each of the 26 events is 1/6 x 1/6 = 1/36.

So the probability that in a given roll of two dice the resulting event is any of the above 26 events is 26/36 = 13/18 = 0.72222... ≈ 72.2%.

What is the probability of pulling a red face card and another red face card out of a full deck?

26 of 52 because there are 52 cards in deck and half of them are red and the other half is black so half of 52 is 26 so there is a probability of pulling a red card 26 out of 52 cards.