John rolls a pair of standard 6-sided dice. What is the probability that the two numbers he rolls are relatively prime? Express your answer as a common fraction.
Great work Ninja :)
sorry EP our guest is right :(
Thanks for the explanation guest. :)
1,1 | 2,1 | 3,1 | 4,1 | 5,1 | 6,1 |
1,2 | 3,2 | 5,2 | |||
1,3 | 2,3 | 4,3 | 5,3 | ||
1,4 | 3,4 | 5,4 | |||
1,5 | 2,5 | 3,5 | 4,5 | 6,5 | |
1,6 | 5,6 |
\(P(relatively \;prime)=\frac{23}{36}\)
.Ah ha I found the site I was looking for!!
https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html
The height which is red is the sine value - it is also the y value on the unit circle
This is becasue
\(sin\theta =\frac{opp}{hyp}=\frac{y}{1}=y\)
The horizontal distance is cosine theta - it is the x valuc of any point on the unit circle
Because
\(cos\theta = \frac{adj}{hyp}=\frac{x}{1}=x\)
So any (x,y) point on this unit circle is given by \((cos\theta,\;sin\theta)\)
.