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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)
Evaluate following limits. Solution Therefore we will taking a look at a couple of one-sided limits in addition to the normal limit here. In all three cases notice
Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day? Solution:
Surface Area with Parametric Equations In this final section of looking at calculus applications with parametric equations we will take a look at determining the surface area o
sin3xcos5xdx
find the value of x for which the distance between the points p(4,-5) and q(12,x) is 10 units
Some important issue of graph Before moving on to the next example, there are some important things to note. Firstly, in almost all problems a graph is pretty much needed.
Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini
The following relation is not a function. {(6,10) ( -7, 3) (0, 4) (6, -4)} Solution Don't worry regarding where this relation came from. It is only on
t=2x/s-7
A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, both head and tail have appeared , and B be the event at most one tail i
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