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GENERAL RULE
A general rule is to subtract the probabilities with an even number of components inside the parentheses and add those with an odd number of components (one or three) to arrive at the probability of events.
Example
Consider a bag containing 4 white and 5 black balls. A man draws 3 balls at random; let us see what is the probability that all three are black?
The total number of ways in which 3 balls can be drawn is 9C3and the number of ways of drawing 3 black balls is 5C3therefore the probability of drawing 3 black balls is given by
P(All three are black)
Consider the following two polynomials in F 17 [x] (a) Use Karatsuba's algorithm, by hand, to multiply these two polynomials. (b) Use the FFT algorithm, by hand, to
in and ap 1,2,3,4,5,6,7,8,9 11,12,13,14,15,16,17,18,19 and like that nonzzero digit find tn Solution) First break the ''n'' number in terms of 10''s power. For e.g if n=3259 wri
The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that dy dx vanishes for some value of x in the interval -1≤x≤1?
prove that 0!=1
Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example Graph y = - 2/5 x + 3 .
1
LAST COST METHOD
Give me an example , please : 1 over 2 , 14 over twenty-eight
Kwai made 5 pints of iced tea. How many cups of tea did he make?
Y=θ[SIN(INθ)+COS(INθ)],THEN FIND dy÷dθ. Solution) Y=θ[SIN(INθ)+COS(INθ)] applying u.v rule then dy÷dθ={[ SIN(INθ)+COS(INθ) ] dθ÷dθ }+ {θ[ d÷dθ{SIN(INθ)+COS(INθ) ] } => SI
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