SOLUTION: A Manufacturer makes three models of a television set, models A, B and C. A store sells 40% of a model A sets, 40% of a model B sets, and 20% of model C sets. Of model A sets, 3

Algebra ->  Probability-and-statistics -> SOLUTION: A Manufacturer makes three models of a television set, models A, B and C. A store sells 40% of a model A sets, 40% of a model B sets, and 20% of model C sets. Of model A sets, 3       Log On


   

Question 353513: A Manufacturer makes three models of a television set, models A, B and C. A store sells 40% of a model A sets, 40% of a model B sets, and 20% of model C sets. Of model A sets, 3 % have stereo sound; of model B sets, 7 % have stereo sound; and of model C sets, 9% have stereo sound. If a set is sold at random, find the probability that it has stereo sound.
Answer by robertb(5830) About Me  (Show Source):
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The probability that a set taken is A is 0.40. Since 3% of these have stereo, the probability that a set taken is A with stereo is 0.40%2A0.03+=+0.012.
Similarly, the probability that a set taken is B with stereo is
0.40%2A0.07+=+0.028, and
the probability that a set taken is C with stereo is 0.20%2A0.09+=+0.018.
Since these events are mutually exclusive, or disjoint, the probability that a set taken has stereo is 0.012+%2B+0.028+%2B+0.018+=0.058.