First we are going to find the equation of the solid line passing trough the points (0, 3) and (2, 4).
Using the slope formula:
Now we can use the point slope formula to complete the line equation:
Since the shaded region is bellow the line , the inequality represented in the graph is
.
Let us first make the sample space for the event A. The Sample Space will be:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5)
(5,1) (5,2) (5,3) (5,4)
(6,1) (6,2) (6,3)
As can be clearly seen the Sample Space for the event A has 30 elements in it.
Now, it is given in the question that the event A has already occurred and we need to find the probability of the event B occurring <u><em>given that the event A has already occurred.</em></u>
Now, as we can see, from the sample space, only 11 events out of the 30 are the events of interest to us. This is shown in bold below:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5)
(5,1) (5,2) (5,3) (5,4)
(6,1) (6,2) (6,3)
Thus, the probability that the event B occurs given that the event A has already occurred is:
In percentage the required probability is 36.7% approximately.
Answer:
The number of palindromes is
when n is even and
when n is odd
Step-by-step explanation:
From the question we are told that
The length of the string is
Generally palindrome is evaluated by considering the first part of a string
When the the length of the string is an even number then
it means that the first part of the string is
Hence the number of bit strings of length n that are palindromes is evaluated as
But When the the length of the string is an odd number then
it means that the first part of the string is
Hence the number of bit strings of length n that are palindromes is evaluated as
Generally each bit could be either 0 or 1
Hence the number of palindromes is
when n is even and
when n is odd