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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)
Now we take up combinations and its related concepts. Combinations are defined as each of the groups or selections which can be made by taking some or all of the
If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3. Ans: 7 Cosec?-2Cot?=7 P.T 7Cot? - 3 Cosec?=3 7 Cosec?-3Cot?=7 ⇒7Cosec?-7=3Cot? ⇒7(Cosec?-1)=3Cot? ⇒7(C
(x+1/x)^2=3 then value of x^72+x^66+x^54+x^36+x^24+x^6+1 is
Prove that A tree with n vertices has (n - 1) edges. Ans: From the definition of a tree a root comprise indegree zero and all other nodes comprise indegree one. There should
2/6
Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function Y t = AK 1-α t L α t a) Set up the underlying nonlinear differen
What are the factors of 956
Round 468.235 to the nearest hundredth ? The hundredths place is the second digit to the right of the decimal point (3). To decide how to round, you must like as at the digit t
Use the maximum flow algorithm to find a maximum flow and a minimum cut in the given network, where the capacities of arc CF, EC , DE and BD are w = 13, x = 7, y =1, a
Michael made 19 out of 30 free-throws this basketball season. Larry's freethrow average was 0.745 and Charles' was 0.81. John made 47 out of 86 free-throws. Who is the best free-th
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