Probability

A two-tailed test is both, upper and lower tailed!

There are eight (8).

all numbers on a die have the same probability to land so any number between 2 and 12 are just as likely as any other number between 2 and 12, just as any other die hase the same probability 2 d20, 2-40 any to are just as likely as the rest. so 0 is the least likely number.

Well, yes, since 0 is impossible to be the sum of 2 dice, it is least likely. So is any other number less than 2 or greater than 12, or a number that is not a whole number. But of those that actually can come up as the sum of 2 dice, 7 is the most likely because there are 6 ways to get it (1 and 6, 2 and 5, 3 and 4, 4 and 3, etc.). The least likely sums are 2 and 12, because each can only occur 1 way (a pair of 1's or a pair of 6's). These are referred 2 by gamblers as snake eyes and box cars.

If you mean 'at least' 2 heads, the probability is 50%. If you mean exactly 2,

the probability is 3/8, or 37.5%.

There are 3 independent coin tosses, each of which is equally likely to come up

heads or tails. That's a total of 2 * 2 * 2 or 8 possible outcomes (HHH, HHT, HTH,

etc.). Of these, 4 include 2 or 3 heads, which is half of 8. Only 3 include exactly 2

heads, so the probability of that is 3/8.

If you draw enough cards then it is very close to 1 - almost a certainty.

13/52*12/51*11/50*10/49

= 1/4*4/7*11/50*10/49

= 440/68600

= 44/6860

= 11/1715

It must be "mutually exclusive" since "non mutually" does not even mean anything!

1/6= 2 because there is only one 2.

Therefore the theoretical probability of not rolling a two is the same as everything but two so 5/6.

720 ways.

4 cards has 5 in it. 2 "5" on each card. means totally 8 of "5" on cards

5/6

It is: 90/9 = 10

Risk

The first letter of the perm can be any of the 4, the second any of the remaining 3, the third either of the remaining 2. There are thus 4 x 3 x 2 ie 24 permutations.

The number one can be used to describe a certain event.

Black

well since the coins have two sides,there is a 50% chance of it landing on heads

It is impossible to calculate such things.

geometry has 8 letters, 2 of which are the same (e)

So, the answer is 8!/2! = 20,160

I am assuming that this die is fair die and the coin is not biased. The probability of getting a number less than 3 is the probability of rolling a 1 or a 2 i.e. 1/6 + 1/6 = 2/6 which simplifies to 1/3. The probability of getting a head when you flip a fair coin is 1/2. Both are independent events, so the probability of getting a number less than 3 and getting a head is 1/3 x 1/2 = 1/6. One can get the same answer from a sample space diagram

It need not be if:

the number of samples is small;

the elements within each sample, and the samples themselves are not selected independently.

A 1 in 6 chance.

Assuming a two-sided coin, and that you make the the toss, the probability of tossing a head or a tail is 100%. The probability of tossing a head is 50%. The probability of tossing a tail is 50%.

Probability of getting a King is 4/52 = 1/13. Having drawn the King, for it to be a Red King, the probability is 2/4 = 1/2. Hence the conditional probability is (1/13)x(1/2) = 1/26

That depends on the numbers you can spin.