Probability

Yes, it can have any non-negative value.

Yes.

4 in 52, or 1 in 13, or about 0.0769

When you take one cracker out of that bag, eat it, and reach into the bag

for another one, the probability that the next animal will match the first one

is

9/29 = about 31% .

R1B1, R1B2, R1B3, R1B4, R1B5, R1B6,

R2B1, R2B2, R2B3, R2B4, R2B5, R2B6,

R3B1, R3B2, R3B3, R3B4, R3B5, R3B6,

R4B1, R4B2, R4B3, R4B4, R4B5, R4B6,

R5B1, R5B2, R5B3, R5B4, R5B5, R5B6,

R6B1, R6B2, R6B3, R6B4, R6B5, R6B6.

The odds are 1 in 200. The probability of winning is 0.005.

It is 6.6

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

He was exiled to St Helena.

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

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.

360%

7

(1/2)3 = 1/8.

They can, so the question is irrelevant.

100%

The total marbles are 60, your mathematical expectation of getting a single blue marble in one try is therefore 17/60. If you grab 7 random marbles, the mathematical expectation is 7 times 17/60. This is the expectation, in an actual experiment you will get more or less than that, but it should be fairly close to the calculated value. (Note that the mathematical expectation in this case isn't even an integer.)

50 - 50

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.

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.

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

4

Yes, it can.

1 out of 2

Yes, they do.