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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)
Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol
state tha different types of models used in operations research.
Prove the subsequent Boolean expression: (x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z Ans: In the following expression, LHS is equal to: (x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨
a sketch of two dimensional system
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA
Find out a series solution for the following differential equation about x 0 = 0 y′′ + y = 0. Solution Note that in this case p(x)=1 and therefore every point is an or
Under this section we will be looking at the previous case for the constant coefficient and linear and homogeneous second order differential equations. In this case we need soluti
A body is constrained to move in a path y = 1+ x^2 and its motion is resisted by friction. The co-efficient of friction is 0.3. The body is acted on by a force F directed towards t
A rescue and ?re squad places a 15 ft ladder against a burning building. If the ladder is 9 ft from the base of the building, how far up the building will the ladder reach? a. 8
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