Question

In a race where 12 cars are running, the chance that car x will win is 1/6, that y will win is 1/10 and that z will win is 1/8. Assuming that a dead heat is impossible, find the chance that one of them will win.

Answer 1

In a race chances of x, y and z to win are:

P ( x ) = 1/6, P ( y ) = 1/10,  P( z ) = 1/8

And because all the events are mutually exclusive, the chance that one of them will win is:

P ( x ) + P ( y ) + P ( z ) = 1/6 + 1/10 + 1/8 =

20 / 120 + 12 / 120 + 15 / 120 = 47 / 120

Answer:

The chance that one of them will win is 47 / 120.

Answer 2

we are given

P ( x ) = 1/6,

P ( y ) = 1/10,

 P( z ) = 1/8

since

all the events are mutually exclusive, the chance that one of them will win is:

P ( x ) + P ( y ) + P ( z ) = 1/6 + 1/10 + 1/8  

taking lcm of these three we get

20 / 120 + 12 / 120 + 15 / 120 = 47 / 120

The chance that one of them will win is 47 / 120.