(a)
To find: the probability that the coin covers a vertex of one of the squares on the grid.
(a)
Answer to Problem 69E
The probability of the coin is
Explanation of Solution
Given information:
A coin of diameter
Given figure
Calculation:
Consider a point
It is clear that the coin covers the vertex when the distance between
Since every gird on the paper forms four quarter circle
The radius of each circle is
Therefore, the area of each circle is given by
Also, since the side of square is
Therefore, the area of each grid is given by
It is clear that
So, the probability of the coin is
(a)
To find: the probability that the coin covers a vertex of one of the squares on the grid.
(a)
Answer to Problem 69E
The probability of the coin is
Explanation of Solution
Given information:
A coin of diameter
Given figure
Calculation:
Consider a point
It is clear that the coin covers the vertex when the distance between
Since every gird on the paper forms four quarter circle
The radius of each circle is
Therefore, the area of each circle is given by
Also, since the side of square is
Therefore, the area of each grid is given by
It is clear that
So, the probability of the coin is
(b)
To approximate: the value of
(b)
Answer to Problem 69E
The area covered by the coin in 100 drops is
Explanation of Solution
Given information:
A coin of diameter
Given figure
Calculation:
In the previous part as it is shown that dropping a coin covers
Since the coin is dropped 100 times.
So the area covered by the coin in 100 drops is
Chapter 8 Solutions
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