This question is a tutorial question of a Statistics module that I have to take as part of my university graduation requirements.
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A game about the impact of climate change on human life uses ten independent rolls of a fair die to simulate the weather for ten years. If the die shows one spot or six spots, then there is a crisis.
(a) Calculate the probability that there is no crisis in a ten-year period, to 2 significant digits.
(b) The quality of life increases by 10 points if there is no crisis in a ten-year period, and decreases by 2 points otherwise. Calculate the average amount by which the quality of life increases after ten years. Interpret this number in terms of a large number of worlds independently controlled by this game.
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Proposed solution based on my understanding:
P(2,3,4,5) = 1/6 + 1/6 + 1/6 + 1/6 = 4/6
P(no crisis) = (4/6)^10 = 0.017.
May I know if the first part of my answer to the question is correct?
Also, assuming the answer above is correct, am I right to say that according to the complement rule, P(crisis) = 1 - 0.017 ?