Difference between revisions of "Answer"
Jump to navigation
Jump to search
Ryan Moruzzi (talk | contribs) (Challenge Problem Answers) |
Ryan Moruzzi (talk | contribs) |
||
| Line 2: | Line 2: | ||
| − | In order for no cats to collide, all four cats must walk in the same direction. Thus, all four cats must walk clockwise OR all four cats must walk counterclockwise. This means <math>P(no cats collide) = P(all cats go clockwise) + P(all cats go counterclockwise)</math>. | + | In order for no cats to collide, all four cats must walk in the same direction. Thus, all four cats must walk clockwise OR all four cats must walk counterclockwise. This means <math>P(no cats collide) = P(<text>all cats go clockwise</text>) + P(all cats go counterclockwise)</math>. |
The probability a cat chooses clockwise or counterclockwise is <math>1/2</math>. So the probability all four cats choose clockwise or counterclockwise is <math>(1/2)*(1/2)*(1/2)*(1/2)</math>. | The probability a cat chooses clockwise or counterclockwise is <math>1/2</math>. So the probability all four cats choose clockwise or counterclockwise is <math>(1/2)*(1/2)*(1/2)*(1/2)</math>. | ||
Therefore, <math>P(no cats collide) = (1/2)*(1/2)*(1/2)*(1/2) + (1/2)*(1/2)*(1/2)*(1/2) = 1/16 + 1/16 = 1/8.</math> | Therefore, <math>P(no cats collide) = (1/2)*(1/2)*(1/2)*(1/2) + (1/2)*(1/2)*(1/2)*(1/2) = 1/16 + 1/16 = 1/8.</math> | ||
Revision as of 10:31, 2 May 2015
Challenge Problem 2 Solution
In order for no cats to collide, all four cats must walk in the same direction. Thus, all four cats must walk clockwise OR all four cats must walk counterclockwise. This means .
The probability a cat chooses clockwise or counterclockwise is . So the probability all four cats choose clockwise or counterclockwise is .
Therefore,
