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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)
Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha
in a garden 1/8 of the flowers are tulips. 1/4 of the tulips are rd. what fraction of the flowers in the garden are red tulips
Find out the next number in the subsequent pattern. 320, 160, 80, 40, . . . Each number is divided by 2 to find out the next number; 40 ÷ 2 = 20. Twenty is the next number.
STATISTICS AND PROBABILITY : Statistics are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of
cosx
nc6:n-3c3=91:4
is 4x-9 a polynomial function?
It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system, x?' = A x? Here the eigenvalues of the matrix A are compl
Trig Functions: The intent of this section is introducing you of some of the more important (from a Calculus view point...) topics from a trig class. One of the most significant
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
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