Posted by Zach on Thursday, May 13, 2010 at 10:58pm.
A good idea is to take 6 identical coins and line them up as above (6 quarters)
draw a line from the centre of the bottom middle circle to the centre of the left circle of the middle row.
Draw a horizontal line from the centre of the left circle in the second row to the point of tangency with the other circle in that row.
Draw a vertical from that point of tangency to the centre of the bottom middle circle.
You should have a right-angled triangle with hypotenuse 1, short leg as 0.5 and vertical leg as x
x^2 + .5^2 = 1^2
x^2 = .73 or 3/4
x = √3/2
so the distance from the outside of the bottom middle circle to the centre of the 6 circles is
√3/2 + .5
Then the height of the whole stack is
2(√3/2 + .5)
= √3 + 1
In a particular game, a fair die is tossed. If the number of spots showing is either four or five, you win $1. If the number of spots showing is six, you win $4. And if the number of spots showing is one, two, or three, you win nothing. You are going to play game twice.
The probability that you win $4 both times is
a)1/6
b)1/3
c)1/36
d)1/4
e)1/12
1/3
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