Odds vs Probablity in Math

October 13, 2008
If you flipped three pennies, what would be the odds that they all came out the same?

 Ok... Odds are different from probability
 Probability(x) = (Chances for)/(Total chances)
Odds, on the other hand, are given as: (Chances for) : (Chances against)

So if these are the following solutions:
TTT (000)
TTH (001)
THT (010)
THH (011)
HTT (100)
HTH (101)
HHT (110)
HHH (111)

There are 2/8 solutions that satisfy this. So 1/4 would be the PROBABILITY, but they asked for ODDS which would be 2:6 or 1:3

How to solve the 2 cars math problem

If two cars were faced away from each other back to back, both cars travelled 8 miles forward then made a 90 degree left turn and traveled another 6 miles, how far apart would they be?

Possible answers (as given on question):

� Right next to each other.

� 48km

� 32km

� I'm not sure / Hey, there's no SKIP button

First we must find how far each car went. If the beginning point is (0,0) on a coordinate plane, the the car on the right went to point (8,6) and the car on the left went to point (-8,-6). They for a diagonal line on opposite sides of the plane so option A (Right next to each other is wrong). We want to find the length of the diagonal so we do the following.

a^2 + b^2= c^2 (the Pythagorean theorem)

a= to the distance on the x axis (or 8) and b= to the distance on the y axis (or 6). Remember, you cannot have negative distance, so even though on of the cars is in the negative portion of the plane, it still went positive distance. C= the unknown diagonal length.

a^2 + b^2= c^2

8^2 + 6^2= c^2

64 + 36 = c^2

100 = c^2

sqrt(100)= sqrt(c^2)

10 = c

c= 10

They are 20 miles away from each other. However, the answers are in km so we convert from mi to km.

1 mile is, approximately, 1.6 km so we do the following:

1 mi/1.6 km = 20 mi/ X km, cross multiply

X= 32

So the distance between the two cars is approximately 32 km, or answer C.