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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?
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
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
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