This page holds a finished MATH-105N Week 6 everyday probability write-up: the sample space built and counted, the probability produced from it, and an expected value carried into a decision. Searches like "math 105n week 6 assignment example", "math105n week 6 sample" and "math-105n week 6 example" land here.
What a finished MATH-105N Week 6 everyday probability write-up looks like
Short worked items with a paragraph of argument at the end, and a visible list underneath every figure. The write-up produces its own numbers rather than reading somebody else's: the sample space is written out or drawn as a tree, the favorable outcomes are marked inside it, and the fraction comes off that count. Where the space is too large to list, the counting rule used to size it is named and applied. Odds appear on a separate line from the probability, because the two are different numbers and sections test whether the writer knows it. An expected value calculation, where the item includes one, lists every payout beside its chance and sums the products. A last paragraph says what a person ought to do with the figure.
How a MATH-105N Week 6 example is structured
Counting needs a described situation, so the write-up settles how many tickets, how many faces, how many names are in the drawing, and whether anything is replaced between draws. The sample space follows, listed in full where it is small and built with a tree diagram where it has stages, because a stage the writer forgot is the commonest source of a wrong denominator. Favorable outcomes are then identified inside that space and counted, not estimated. The probability is written as a fraction and again as a decimal or a percentage, with a clause naming which event it is the probability of. Combined events come next, and a sentence settles whether one draw changes the next before any multiplying happens. Expected value closes the mathematics, and a short paragraph closes the item by naming the decision the figure supports.
The sample space, written not assumed
Small spaces are listed in full and staged ones are drawn as a tree. A figure with no visible space behind it is an assertion, and these rows pay for the counting.
Favorable outcomes counted inside it
The favorable cases are marked within the same list the denominator came from. Counting them off a different description is how two numbers end up measuring different things.
Odds and probability kept apart
Three to one against and one quarter describe the same situation in different arithmetic. Items usually ask for both, and treating them as interchangeable loses the row outright.
Independence settled before multiplying
Drawing with replacement and drawing without are different problems. One sentence deciding which applies protects every product that follows it.
Expected value, then the recommendation
Each payout sits beside its chance and the products are summed. The closing sentence says whether the arrangement is worth entering, which is what an applied course is asking for.
Where marks go in MATH-105N Week 6
The largest forfeit belongs to a probability asserted without the outcomes ever being listed, because the list is the deliverable and the fraction is only its summary. Running close behind is a sample space missing a stage, which produces a clean fraction over the wrong denominator and survives any check of the arithmetic. Items multiplying two chances together with no sentence on independence lose the reasoning row even where the product happens to be right. Treating odds and probability as one number costs a row every time it appears, since three to one and three quarters are different claims. An expected value omitting one payout is wrong by exactly that term and still looks complete. And a write-up stopping once the figure exists, recommending nothing, drops the applied half of the week.
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MATH-105N Week 6 questions, answered
Does the write-up ever need a formal counting formula?
Only where the space is too large to list, which most items in this week avoid on purpose. Where one is needed, the finished version names it, says what is being chosen from what, and states whether order matters, since that single decision changes the count. Listing a small space in full remains better than a formula nobody reading it can check.
How is expected value presented when the payouts are not money?
The same way, with the unit carried through. Hours saved, seats filled and miles driven all behave like dollars inside the sum, provided every outcome is measured in the same thing. The finished item names that unit once at the top and attaches it to the final figure, because an expected value with no unit cannot be compared against anything.
What does a section mean by an everyday situation here?
Something a reader could be standing in front of: a raffle at a school event, a warranty offered at a counter, a spinner in a game, a drawing for a parking space. The mathematics is identical to the textbook version; what changes is that the closing sentence has to recommend something, and a vague situation gives it nothing to recommend.