In the CSU system, 78% of the students are California residents. Two CSU students are to be chosen at random. You might wish to sketch a tree diagram on scratch paper to help answer the following. Find the probability that...
a) ...both are California residents.
b) ...one is a California resident and the other is not.
c) ...neither is a California resident.
d) ...at least one is a California resident.
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To answer these questions, we can use a tree diagram to visualize the different possible outcomes.
a) To find the probability that both students are California residents, we multiply the probability of the first student being a California resident (0.78) by the probability of the second student also being a California resident (0.78). So the probability is 0.78 * 0.78 = 0.6084.
b) To find the probability that one student is a California resident and the other is not, we have two cases: California resident - non-resident or non-resident - California resident. For the first case, we multiply the probability of the first student being a California resident (0.78) by the probability of the second student not being a California resident (1 - 0.78 = 0.22). For the second case, we do the opposite. So the probability is 0.78 * 0.22 + 0.22 * 0.78 = 0.3432.
c) To find the probability that neither student is a California resident, we multiply the probability of the first student not being a California resident (1 - 0.78 = 0.22) by the probability of the second student also not being a California resident (0.22). So the probability is 0.22 * 0.22 = 0.0484.
d) To find the probability that at least one student is a California resident, we subtract the probability that neither student is a California resident (0.0484) from 1. So the probability is 1 - 0.0484 = 0.9516.
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