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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)
Verify Liouville''s formula for y "-y" - y'' + y = 0 in (0, 1) ?
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
8y square minus2
Using the same mean and standard deviation from problem 10 (mean m = 20.1 and a standard deviation s = 5.8). Joe was informed that he scored at the 68 th percentile on the ACT, wh
100 plus 2
Find no. of non negative integral solutions x 1 +x 2 +x 3 +4x 4 =20 Solution) 140. Break them into prime factors . Put 4 = 2^2 and every variable will have factors in 2,3,5 with
Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one? Solution: There are 10 wa
economic order quantities (EOQ) Statistics may be utilized in ordering or making economic order quantities as EOQ. It is significant for a business manager to understand that
how do you do algebra with division
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
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