Calculate dice-event, union and conditional probabilities.
Calculate dice-event, union and conditional probabilities.
7 marks
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Two fair dice are thrown and the number showing on each is noted. The sum of these two numbers is S. Find the probability that
S is less than 8;[2]
at least one die shows a 3;[2]
at least one die shows a 3, given that S is less than 8.[3]
Solution:
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Answer:There are 11 outcomes with at least one 3, giving \(\frac{11}{36}\). Seven of these also have \(S<8\), so the conditional probability is \(\frac7{21}=\frac13\).