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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)
(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which
Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
Ask question #Minimum 100 words accepted what is a ratio
1. A 3d rotation matrix has 9 (3 by 3) entries, and a 2d rotation matrix has 4 (2 by 2) entries. How many actual degrees of freedom are there in a 3d or 2d rotation? In other words
A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"
How do you solve a table to get the function rule?
Max can paint a house in 3 hours. Saria can paint a house in 5 hours. working together, how long will it take both Saria and Max to paint a house?
Write a script to determine the volume of a pyramid, which is 1/3 * base * height, where the base is length * width. On time the user to enter values for the length, width, and th
if a+1/b=b+1/c=c+1/a then the value of abc is
Generate a 1000 vertex graph adding edges randomly one at a time. How many edges are added before all isolated vertices disappear? Try the experiment enough times to determine ho
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