Another maths question??? Plz help...THANX!?

A fair die is altered so that the 1 is changed to a 5. If X is the random variable representing the number uppermost on the die, find:


(a) the probabiliy distribution of X


(b) the probability of a number bigger than 2 appearing uppermost


(c) P(X = 5 | X %26gt; 2)





I know how to do (a) and (b)...but I don't know how to do (c). In my maths book, it says that (c) has something to do with the conditional probability, which I don't have any clue about.





This is the conditional probability rule stated in my textbook:


P(X = x | X %26gt; n) = [P(X = x ∩ X %26gt; n)] / P(X %26gt; n)





Can someone please explain whatever this is??? AND this "∩" sign...I don't understand what it means!?!

Another maths question??? Plz help...THANX!?
Victory..I just arrived home..exhausted from school.


this is a conditional probability..i think...it's not our lesson, but i read it somewhere..but can't remember..


that long equation stated in your book is :





P(X=x | X%26gt;n) = [P(X=x ∩ X %26gt;n)] / P (X%26gt;n)





is the same as:





P(B | A)= [P (A "and" B)] / P (A)





(..i think in intersection, terms can be interchanged?.)





..which is a lot simpler and easier to understand..


Hey you might want to know how the formula is derived.


it's like this:





1. P (A ∩ B) = P (A) * P (B|A)





2.[P (A ∩ B)] / P(A) = [P (A) * P (B|A)] / P(A)





-divide both sides of equation by P(A)





3.cancel the P(A) / P(A) on the right portion of equation so..





[P (A ∩ B)] / P(A) = P (B|A)





4. P (B|A) = [P (A ∩ B)] / P(A)





...(that's it, and I just commuted it..)





so this sign: ∩ is an intersection sign, and is also read as "and".





so let's substitute the values okay?


----------------------


in P(X=5|X%26gt;2)..is 2/6


and


P(X=5 and X%26gt;2) is 5/6





(refer to the explanation of the guy above me)





hmm..


that should do it..(i think)





P(X=5 | X %26gt; 2) = [P (X=5 ∩ X%26gt;2)] / P(X%26gt;2) = (2/6)/(5/6)





since we divide both fractions, we get the reciprocal of denominator then multiply


2/6•6/5=12/30=2/5





P(X = 5 | X %26gt; 2) = 2/5
Reply:P(X = 5 | X %26gt; 2) = 2/5





This is because 5 of the 6 possibilities have x %26gt; 2 and 2 of those 5 have x=5.





Using the notation of your book, P(X = 5 | X %26gt; 2) = [P(X = 5 ∩ X %26gt; 2)] / P(X %26gt; 2)





The " ∩ " means intersection, or in this case, [P(X = 5 ∩ X %26gt; 2)] means the probability that X=5 and X%26gt;2, which is 2/6. So using the formula, we get P(X = 5 | X %26gt; 2) = [P(X = 5 ∩ X %26gt; 2)] / P(X %26gt; 2) = (2/6)/(5/6) = 2/5
Reply:Conditional probability means


P(a | b) which means


the probability A will occur when we know that B has already occured.





Apply this to ur Question c part.


It now reads: Probability that 5 will appear when we know that the number appearing is greater than 2.





How many nos are greater than 2 on the dice. 3,4,5,5,6 ie. 5





So the probability that 5 will appear is 2/5.





Hope this helpd.








TW K

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