# A wheel of fortune has six closed compartments arranged round the circle. When it is spun, a compartment is selected uniformly at random. Initially, two adjacent compartments each contain Rs 1000. Players A and B take turns to play. Player A spins the wheel, but ?nds the selected compartment empty. Player B now has a choice of either spinning the wheel again or else rotating the wheel to the opposite compartment. Which choice gives B the better chance of ?nding Rs 1000? What are the corresponding probabilities?

Bhuvi Gupta
18 Points
11 years ago

let the compartmennts be M, N, O, P, Q, R

LET THE MONEY BE IN N AND O

THEREFORE A LANDS AT EITHER AT M,P,Q OR R

LET A LAND AT M/P

1 ROTATION/4 ROTATIONS WILL MAKE HIM REACH AT N/O

NOW LET A LAND AT Q/R

2/3 ROTATIONS WILL MAKE HIM REACH N/O

THEREFORE WE SEE THAT FOR ANY RANDOM COMPARTMENT,

IF HE ROTATES THE WHEEL THE PROBABILITY OF HIM GETTING THE MONEY IS 1/4

BUT IF HE SPINS THE WHEEL THE PROBABILITY BECOMES 2/6=1/3

THEREFORE THE PROBABILITY OF GETTING THE MONEY IS MORE IF HE SPINS THE WHEEL