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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 do you plot your boat's estimated position?
There appears to be some confusion regarding DR plots and IT (Intended Track) plots as well as how they apply to an EP.
A basic estimated position is based on a DR plot (time and speed only, no current, tide, leeway or other corrections applied) and the LOP (with bearing and time noted). When drawn, it is done by dropping a perpendicular from your DR position at the time of the LOP (shortest distance). The intersection of the perpendicular and the LOP is your estimated position. I tell my students that this is their "best guess" - then ask them what are the conditions around and ahead of the vessel (are the standing into danger) and what is or will be available to confirm/deny the EP.
The same can be done if you have a Circle of Position (COP) - but, if you have a COP from an object, you should have both the bearing and the range, which by definition is a fix, so no need to do the EP.
Once you have an EP, you do NOT redraw the DR plot. After all, it is not a fix - you do not know if you are really at this position. The only thing that you are sure of is that you are somewhere on the LOP. You may be on either side of the DR plot. You may take action if, based on the EP, you believe that you are standing into danger. I suggest that my students then look at the chart and determine when there will be something else to use for another LOP. Using the second LOP, you then have enough information to generate a running fix.
If you have drawn an DR plot and then corrected it for local tide and current conditions, this is usually called an Intended Track (IT) plot. Normally, you see this when there are significant known currents or leeway conditions. In that case, the original DR is known as the IT and the new DR is the one that you are going to steer to get you through the conditions. You provide instructions to the helmsperson to steer the second track, and the currents/tides should push your vessel down the first track (you are crabbing through the water). In this case, if you have a single LOP, you determine your EP based on the IT plot (the first DR plot), as this is where you WANT TO BE (should be) after taking into account tides, currents and leeway. In this situation, at the first fix, you should calculate the actual set/drift of the currents - because they will be different than what is reported in the Coast Pilot.
EPs are good pieces of information to have, but remember that this is a "best guess" as to your position. The actions that most folks would take is to look at the chart and determine what other information is available to confirm/deny the EP. For example, are there other buoys/aides/land marks to take another LOP? Is there sufficient change in the bottom depth (sharp gradients) or type (mud, rock, sand, etc.) for a depth reading to confirm the EP.
I have seen EPs that placed me on one side of by DR plot and have later fixes (10 minutes or so later), put me way on the other side. This has happened several times this year, even though I have drawn both DR and IT plots using currents recorded in the Coast Pilot. This is because the currents have changed so much (lots of rain and other runoff). Using the CP determine the local current data is a good GUIDE, but this is based on a multi-year running average. So if you are boating in an area that has experienced significant rain, storms (Ivan, etc.) or significant drought, the currents will not be what are projected. You can plan your DR/IT plots ahead of time, but need to confirm set/drift by plotting a couple of fixes to doing the math. Then redraw the DR/IT plots based on the actual conditions.
I know that there are others much more knowledgeable than myself on this, but I hope it helps.
What is the probability of not rolling a 5?
Even if I assume that you mean probability and not probility, the question cannot be answered since there is no information as to what is being rolled. For a normal tetrahedral die, the answer is 1.
The liklihood of an event occurring?
Placing a question mark at the end of a phrase does not make it a sensible question.
How many 10's are in a deck of cards?
There are four 10's in a regular deck of 52 playing cards. One for each suit of hearts, diamonds, spades, and clubs.
You probably mean the Greek letter sigma since this is the probability area.
- Lower-case sigma is usually reserved to represent a population standard deviation. When it is squared it represents a population variance. With a caret ('hat') over it it represents an estimator of the population standard deviation.
- Upper-case sigma is most often used to mean summation (adding up) of terms given by the expression after the sigma. The limits of summation are given above and below the sigma symbol in terms of one of the variables in the expression.
1/12 = 0.08333... ≈ 8.33%
p(1,3) = 1/6 (1/6) = 1/36
p(3,1) = 1/6 (1/6) = 1/36
p(2,2) = 1/6 (1/6) = 1/36
p((1,3)u(3,1)u(2,2)) = 1/36 +1/36 +1/36 = 3/36 = 1/12
true
What is the definition of correlation?
If two things correlate or are correlated , they are closely connected or strongly influence each other. correlation-noun
What is the probability of obtaining a sum of at least 5 when rolling a pair of dice?
There is a 1in 36 chance of rolling 2, a 2 in 36 chance of rolling 3 and a 3 in 36 chance of rolling 4. So there is a 30 in 36, or 5 in 6 chance of rolling at least 5 with a pair of fair dice.
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There is only 1 way of scoring 2 (1 and 1).
3 can be scored 2ways (1 & 3 and 3 & 1)
4 is possible 3 ways (1 & 3; 3 & 1; 2 & 2)
5 has 4 ways (1 & 4; 4 & 1; 2 & 3; 3 & 2)
6 has 5 ways (1 & 5; 5 & 1; 2 & 4; 4 & 2; 3 & 3)
7 has 6 ways (1 & 6; 6 & 1; 2 & 5; 5 & 2; 3 & 4; 4 & 3)
8 has 5 ways;9 has 4 ways; 10 has 3 ways; 11 has 2 ways; 12 has only 1 way.
That totals 36 possible ways of scoring with two dice.
So score 2 has probability 1/6; 3 has probability 2/6 = 1/3; 4 has probability 3/6 = 1/2; 5 has probability 4/6 = 2/3.
We want to know the probability of scoring less than 5, which has 6 ways out of 36 = 1/6
Now, all the probabilities must total exactly 1, so the probability of scoring at least 5 must be 1 - 1/6 which is 5/6 = 0.83333333333 (the 3 reoccurs ) = 83.33333(recurring)% or just over 83%
1001 is the lowest four-digit palindrome, which is 0 modulus 7. Adding one to the first and last digits adds 0 modulus 7. Adding one to the second and third digits adds 5 modulus 7, since 110 is also 5 modulus 7. So only 770 plus multiples of 1001 are divisible by 7.
Out of 90 possibilities, there are only 9 that are divisible by 7. So the probability is 9/90, or 1/10.
What are the dimensions of a 5/4 deck board?
A 5/4 deck board typically has a thickness of 1 inch and a width of 4 inches.
What is a game tree and how does it represent the possible outcomes and decisions in a game?
A game tree is a visual representation of the possible outcomes and decisions in a game. It shows all the possible moves that players can make at each decision point, branching out into different paths based on those choices. This helps players analyze and strategize their moves by considering the potential consequences of each decision.
