Which hand?
Martha holds a ball in her left hand.
Every second she has a 90% probability of moving the ball to the opposite hand that it is in.
What is the probability that the ball will be in her right hand after 7 seconds?
Give your answer to 3 decimal places.
So, for example, after one second she has a 90% chance of the ball being in her right hand. So, in this case, you would submit 0.9 as your answer.
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The answer is 0.605.
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1 solution
Define, R n = probability the ball is in her right hand after n seconds.
Then, R 0 = 0 .
Now, every second, the probability of the ball being in her right hand is given by 0.9 times the probability that it is in her left hand plus 0.1 times the probability that it is in her right hand.
And, for n > 0
R n = 0 . 9 L n − 1 + 0 . 1 R n − 1
R n = 0 . 9 ( 1 − R n − 1 ) + 0 . 1 R n − 1
Solving,
R 7 = 0 . 6 0 5