Sunday, 12 January 2014

probability - Rolling a die, expected number of coins won



So this is a problem I'm stuck on,




You roll a fair 4-sided die and with probability 1/3 you get to roll once more, and with probability 2/3 you have to stop.
Assume that you get as many coins as the sum of the rolls.
What is the probability you will win an even number of coins?



Can somebody help?



PS: You can get as many extra rolls as possible!


Answer



With a coin, at a probability of 1/4 you flip it and at a probability of 2/4 you stop. With a four-sided die, at a probability of 1/3 you get one more roll and at a probability of 2/3 you stop. If you multiply those together, you get 2/4*2/3=4/12=1/3, which is the probability of where you roll a four-sided die one more time. Also, 2/4 is equal to 1/2, which is the probability of flipping a coin.



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