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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

If you roll a six sided dice six times you will roll an even number at least once True or False and how did you get it?

You have a 3.125% chance of not rolling an even number, because each time you roll a die you have a 50% chance of not rolling an even number, but each additional time you roll a die your chances of not rolling an even number the formula changes from 3/6 to 3/12 because the possibilities double but your chances of not rolling an even remain the same so eventually we end up with 3/96 because of rolling the die 6 times.

How can study more than 15 hours per day.?

Well it will be hard or is should say very hard but it is not impossible.

like straight after coming for school then sit straight for study and create a atmosphere that you are in a exam and study for 3 hours not even getting up for drinking water then take a break and think what you would achieve by studying this much during break and again study.

Hope it will be useful.

Who is on the head and tail side of the penny?

The head of a penny is obviously the queens head, and the tail is that thing on the other side of the penny.

What do you mean by step and touch potential and it's standard value?

Step Potential is the potential Difference between two points on the earth's surface, separated by distance of one pace, that will be assumed to be one meter in the direction of maximum potential gradient (IS 3043) Touch Potential is the potential difference between a grounded metallic structure and a point on the earth's surface separated by a distance equal to the normal maximum horizontal reach, approximately one meter. (IS 3043)

What is the probable explanation for referred pain?

Nerves carry the signal to other body parts so your brain interprets the pain from being from that distal part also.

Decision making theory?

Decision making theory is used to determine the values and other issues, including uncertainties, that relate to the decision being made. It is then determined if the decision is a rational and wise decision to be made.

What is probably being misunderstood by a person who says but that's only a scientific theory?

Nearly 100%. Someone who claims something is "just a theory" has already proven they lack an understanding of scientific definitions. This usually means they lack an understanding of the subject which they refered to as just a theory.

How many different ways can all of the letters of a nine letter word be arranged?

Factorial 9 (9!), ie 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 different ways, that's 362880!

What is the probability of rolling a die 120 times and getting 5 or 6?

It is 1 - pr(no 5 nor 6 in 120 rolls)

= 1 - (2/3)120

= 1 - 1.113*1057

which is so close to 1 as to make no difference.

It is 0.99...98887 which starts off with a string of 56 nines.

What is the probability that at least one die shows a 4 or that the sum of the dice is greater than 5?

Assuming:

  • you are rolling two six-sided dice:
  • "greater than 5" does not include 5

Number of possible rolls = 36 (6x6)

28 rolls satisfy "at least one die shows a 4 or the sum of the dice is greater than 5":

(1, 4), (1, 5), (1, 6),

(2, 4), (2, 5), (2, 6),

(3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (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 that at least on die shows a 4 or that the sum of the dice is greater than 5 is 28/36, or 7/9, or approx. 77.8%

In a six sided die what is the possibility of rolling 2 odd numbers in a row?

There are 3 odd (1,3,5) and 3 even (2,4,6) sides on a 6-sided die.

When rolling a 6-sided die, each face has an equal chance of coming up (assuming a perfect die).

Because of this, the chance of rolling an odd number once is 50%.

The second roll you again have a 50% chance to roll an odd number, which means that the chance to roll two in a roll is (50% * 50%) 25%.

1/2*1/2 = 1/4 =

25%

In other words, the chance of rolling an odd number is 1/2 to the Nth power, where N is the number of rolls.

Rolling a dice 10 times means a chance of (1/2)n10 or

1/2 *1/2 *1/2 *1/2 *1/2 *1/2 *1/2 *1/2 *1/2 *1/2 =

1/1024 =

0,097%

Why are variables represented as letters?

Variables are represented as letters so they don't get confused with numbers.

How can you use simulations to estimate probability?

Experimental or empirical probability is estimated from repeated trials of an experiment. However, instead of actually carrying out the experiment a very large number of times, it may be possible to simulate them.

How do you determine the possiblitiy of four outcomes?

To determine the possibility of four outcomes, you first assess the total number of potential outcomes in the scenario. Then, you can calculate the probability of each specific outcome by dividing the number of favorable outcomes by the total outcomes. If the outcomes are equally likely, each outcome has a probability of 1 divided by the total number of outcomes. Additionally, you can use combinatorial methods or simulations to further analyze the likelihood of each outcome occurring.

Proof of angle sum property of a regular quadrilateral?

A regular quadrilateral has 4 angle and their sum must be 360 degrees by the general formula 180 degrees (n-2) for the number of angle in an n sided polygon. So there are 180(4-2)=360 degrees. Since it is regular this means each angle is 360/4=90 degrees.

If you have 10 numbers 0 through 9 only can use 4 at a time like this 2579 and you can also use a number more than once like this 4676 how many different combos are there?

In this problem, think of it as being able to select 0-9 for each of the 4 numbers. So, you can select 10*10*10*10 = 10,000 combinations. If you could not use a number twice, it would be 10*9*8*7.