SOLUTION: A random experiment has sample space S ={a, b, c}. Suppose that P[{a, c}] = 5/8 and P[{b, c}] = 7/8. Use the axioms of probability to find the probabilities of elementary even

Algebra ->  Probability-and-statistics -> SOLUTION: A random experiment has sample space S ={a, b, c}. Suppose that P[{a, c}] = 5/8 and P[{b, c}] = 7/8. Use the axioms of probability to find the probabilities of elementary even      Log On


   

Question 363454: A random experiment has sample space S ={a, b, c}. Suppose that P[{a, c}] = 5/8 and P[{b, c}] = 7/8. Use the axioms of probability to find the probabilities of elementary events.
Answer by robertb(5830) About Me  (Show Source):
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P[{a,b,c}] = P[{a,c}] + P[{b,c}] - P[{c}]. Thus 1+=+5%2F8+%2B+7%2F8 - P[{c}]. Hence P[{c}] = 1/2. Now P[{a,c}] = P[{a}] + P[{c}], so P[{a}] = 1/8. Finally, P[{b}] = 1-1%2F2-1%2F8+=+3%2F8.