1. In a certain school, four levels of French are taught, with 36% of the studen

Question

1. In a certain school, four levels of French are taught, with 36% of the students being enrolled in level 1, 32% being enrolled in level 2, 20% enrolled in level 3, and 12% enrolled in level 4. The percent of people who enjoy their French class is 67% in level 1, 84% in level 2, 82% in level 3, and 93% in level 4. Given that a person enjoys his/her French class, what is the probability the student is enrolled in level 3?

2. Roll a blue die and a red die. Given that the blue die has an odd value, what is the probability that the sum of the two dice is exactly 8?

3. Two fuses in series are built to shut down if an overload occurs. If the first fuse shuts down properly 91% of the time, there is no need for the second fuse to do anything. If the first fuse fails to shut down properly, the second fuse suts down properly 90.1% of the time. What is the probability the whole system operates correctly during overloads (with one or the other shutting down properly)?

Explanation / Answer

1.

Let

1,2,3,4 = the levels
E = enjoys

Hence,

P(E) = P(1) P(E|1) + P(2) P(E|2) + P(3) P(E|3) + P(4) P(E|4) = 0.36*0.67 + 0.32*0.84 + 0.20*0.82 + 0.12*0.94

P(E) = 0.7868

Hence,

P(3|E) = P(3) P(E|3) / P(E) = 0.20*0.82/0.7868 = 0.208439248 [ANSWER]

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