Probability

Part1: Finding probability of getting sum as a perfect square.

Maximum sum of both the dice is (6+6) equal to 12.

Up to 12, the perfect squares are: 1, 4 and 9.

Getting a sum of 1 from two dice is not possible. So, we are left with 4 and 9.

To get 4, the combination can be: (2,2) or (1,3) or (3,1). This means, to get the sum as 4, the probability is [3/36].

To get 9, the combination can be: (3,6) or (6,3) or (5,4) or (4,5). This means, to get the sum as 9, the probability is [4/36].

Therefore,the total probability of getting the sum as a perfect square is: [(3/36)+(4/36)]=[7/36].

Part2: Finding the probability of getting sum as an even number.

The possible even numbers can be 2, 4, 6, 8, 10 and 12. But, as 4 is already considered in part1, it should be ignored in this case.

The probability of getting sum as 2 is: [1/36]

The probability of getting sum as 6 is: [5/36]

The probability of getting sum as 8 is: [5/36]

The probability of getting sum as 10 is: [3/36]

By adding all the above, the probability of getting sum as an even number (ignoring 4) is:

[(1/36)+(5/36)+(5/36)+(3/36)]=[14/36].

From part 1 and part 2, we get the total probability as [(7/36)+(14/36)]=[7/12]=0.583333.

The expected value is the average of a probability distribution. It is the value that can be expected to occur on the average, in the long run.

It would be 3*5 = 15.

It means the two events cannot simultaneously occur; for example the two events, being dead and being alive are mutually exclusive, since they cannot occur at the same time.

gregor mendel

True.

If the odd favoring an event are 10 to 1, then the probability of the event occurring is 0.9.

The odds in favor of an event are 10:1.

Find the probability that the event will occur.

----

P(E)+P(E') = 1

---

P(E)/P(E') = 10/1

So P(E) = 10P(E')

----

Substitute for P(E) and solve for P(E'):

10P(E')+P(E') = 1

11P(E') = 1

P(E') = 1/11

---

Therefore P(E) = 10/11

35:1 or 35 to 1.

"Snake eyes"

The probability for a total of two on two dice are the product of the chances

on each die. You will get one spot an average of one time in six on

one die, so the chances are one in 6. The same is true on the second

die, so the chance of both happening together on one roll are 1/6 x 1/6

or 1/36.

"On average,"1 out of 36 times you will get "snake eyes," so 35 out

of 36 times you will not.

That make the odds AGAINST equal 35:1 or 35 to one.

Answer: 17 to 1

Out of 36 possibilities for two dice, a total of three

can be made by

1 + 2 OR

2 +1

That makes the chances FOR equal to 1/36 plus 1/36, or 2/36 or 1 in 18 throws.

The odds against are therefore 17 to 1.

"On the average," you will 17 non-threes for each three.

Assuming that the die is a "normal" one (it has the numbers 1 to 6 and that it is fair), then the probability of rolling six three times in a row is 1/6*1/6*1/6 = 1/216 = 0.00463

The probability of rolling six three times in a row eventually is 1 (ie a certainty).

I am guessing that a theoretical assertion is made when one states something that is not fact as if it were fact.

More than you'd believe! The first book can be any one of twenty, the second any one of the remaining nineteen and so on until the fifteenth book can be any of the last six.

This is 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 different arrangements, which multiplies to a 17-digit number!

20,274,183,401,472,000 or "twenty quadrillion, two hundred and seventy four trillion, one hundred and eighty three billion, four hundred and one million, four hundred and seventy two thousand" (in US figures).

Do not attempt to check it in your local library!

Probability = number_of_white_marbles / total_number_of_marbles

= 10 / (4 + 6 + 4 + 10)

= 10 / 24

= 5/12

~= 0.42

The first dice can show any number. However the second dice has a 1 in 6 chance of being the same as the first.

Hence the probability of getting two numbers the same is 1/6.

24 red marbles

Flipping a coin is a 50-50 chance no decision or thought needed. A jury should have the right of mind not to base a conviction on luck they have to decide for themselves and weight the options. It is not a just process to take the lives of others in the hands of chance.

22 marbles are in the fifth line.

Low back pain

random sample is a big sample and convenience sample is small sample

2 out of 3 times 3 out of 5

98.73

That depends on the size of the marbles, as well as the size and shape of the jar.

According to the central limit theorem, as the sample size gets larger, the sampling distribution becomes closer to the Gaussian (Normal) regardless of the distribution of the original population. Equivalently, the sampling distribution of the means of a number of samples also becomes closer to the Gaussian distribution. This is the justification for using the Gaussian distribution for statistical procedures such as estimation and hypothesis testing.

It is an ordered pair of the form (A, n) where A is the outcome of the tossed coin (H or T) and n is the outcome of the rolled die (1, 2, 3, 4, 5, 6).