The sum of four times a first number and eight times a second number is 64. If the second number is subtracted from four times t
1 answer:
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The correct question statement is:
A probability experiment is conducted in which the sample space of the experiment is S = {4,5,6,7,8,9,10,11,12,13,14,15}. Let event E={7,8,9,10,11,12,13,14,15}. Assume each outcome is equally likely. List the outcomes in
. Find 
.
Solution:
Part 1:
means compliment of the set E. A compliment of a set can be obtained by finding the difference of the set from the universal set. The universal set is the set which contains all the possible outcomes of the events which is S in this case.
So, compliment of E will be equal to S - E. S - E will result in all those elements of S which are not present in E. So, we can write:
Thus the set compliment of E will contain the elements {4,5,6}.So
= {4,5,6}
Part 2)
means probability that if we select any number from the Sample Space S, it will belong the set E compliment.
= (Number of Elements in 
)/Number of elements in S
Number of elements in set S = n(S) = 12
Number of elements in set = 
=3
So,
A probability experiment is conducted in which the sample space of the experiment is S = {4,5,6,7,8,9,10,11,12,13,14,15}. Let event E={7,8,9,10,11,12,13,14,15}. Assume each outcome is equally likely. List the outcomes in
Solution:
Part 1:
So, compliment of E will be equal to S - E. S - E will result in all those elements of S which are not present in E. So, we can write:
Thus the set compliment of E will contain the elements {4,5,6}.So
Part 2)
Number of elements in set S = n(S) = 12
Number of elements in set
So,
Answer:
f(n) = 2n - 3 describes the arithmetic sequence,
-1, 1, 3, 5, 7, 9, 11, 13,.......
Step-by-step explanation:
Function:
A function is like a machine that gives an output for a given input.
A function has an independent variable which is called the input of the function.
The output for a given input is called the dependent variable.
Here. 'n' is the independent variable
f(n) is the function dependent variable i.e function of n as an output.
For Arithmetic sequence
Where
= nth number of the sequence.
a₁ = First term
d = common difference = a₂ - a₁ = a₃ - a₂ = so on
For a function which describes Arithmetic sequence,
a₁ = -1
d = 1 - -1 =2
∴ f(n) = a₁ + (n -1 )d
substituting the values we get
∴ f(n) = -1 +(n-1)2
using distributive property
∴ f(n) = - 1 + 2n - 2
∴ f(n) = 2n - 3 ..........is the required function