Complete a dice tree and apply a binomial model to repeated occurrence of an event.
Complete a dice tree and apply a binomial model to repeated occurrence of an event.
12 marks
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A pair of fair dice is thrown.
Copy and complete the tree diagram below, which shows the possible outcomes. Let E be the event that exactly one four occurs when the pair of dice is thrown.[3]
Calculate \(P(E)\). The pair of dice is now thrown five times.[3]
Calculate the probability that event E occurs exactly three times in the five throws.[3]
Calculate the probability that event E occurs at least three times in the five throws.[3]
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Answer:For five pairs of dice, \(P(X=3)=0.1118\), while \(P(X\ge3)=0.1350\).