Karl and Naomi roll three dice. Karl gives $10 to Naomi if the number 5 turns up once, twice or three times. Naomi gives Karl $3 in all other cases.

A) construct the probability tree for this situation.

B) Does Karl have an advantage in this game? Justify your answer. My problem is I am unfamiliar on how to draw this probability tree and seem to be having a lot of difficulties, when you have a chance please answer this math problem and get back to me with the results.

Thank you very much for your time and patients.

Secondary(11)

Student



Hi,

I also would draw a probability tree to analyze this problem. On the first roll of the die you could construct 6 branches for the tree, one for each of the 6 possible outcomes. But you only want to know if the result is a 5 or not, so you can construct the tree starting with 2 branches, one for the result of rolling a 5 and the other for the result of not rolling a 5. The same is true for each of the 3 rolls. At each step you only need 2 branches.

On each roll the probability of rolling a 5 is  1/6 and the probability of not rolling a 5 is  5/6. I started the tree below.

I hope this helps,
Penny

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