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Mathematics 9 Online
OpenStudy (anonymous):

(a) From a stack of 3 dice, one is taken and rolled twice. If, unknown to the gambler, two of the dice are weighted and each have a 1/10 chance of rolling a 6, what is the probability that the gambler rolls two 6's? (b) If the gambler has rolled two sixes, what is the probability that he has rolled the weighted die?

OpenStudy (kropot72):

(a) The probability of choosing the fair die is 1/3. If the fair die is chosen the probability of rolling two sixes is 1/6 * 1/6. The overall probability of choosing the fair die is \[\frac{1}{3}\times\frac{1}{6}\times\frac{1}{6}=\frac{1}{108}\] The overall probability of choosing a weighted die and rolling two sixes is \[\frac{1}{3}\times\frac{1}{10}\times\frac{1}{10}=\frac{1}{300}\] The probability of the gambler's rolling two 6's is \[P(two\ 6's)=\frac{1}{108}+\frac{1}{300}+\frac{1}{300}=you\ can\ calculate\]

OpenStudy (anonymous):

can i get help with b) @kropot72

OpenStudy (kropot72):

(b) Given that two 6's have been rolled, the probability that a weighted die was rolled is given by\[P(a\ weighted\ die\ was\ rolled)=2\times(\frac{1}{300}\times\frac{2700}{43})=you\ can\ calculate\]

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