NDA2010MathematicsProbabilityActual
An observed event B can occur after one of the three events A ₁, ~A ₂, ~A ₃ . If P ( A ₁ )= P ( A ₂ )=0.4, P ( A ₃ )=0.2 and P ( B A ₁ )=0.25, P ( B A ₂ )=0.4 , P ( B A ₃ )=0.125 , what is the probability of A ₁ after observing B?
Options
- A1 / 3
- B6 / 19
- C20 / 57
- D2 / 5
Correct answer
C. 20 / 57
Step-by-step solution
aligned & P ( A ₁ ~B )= P ( A ₁ ) P ( B A ₁ ) P ( A ₁ ) P ( B A ₁ )+ P ( A ₂ ) P ( B A ₁ ) & = 0.4 0.25 0.4 0.25+0.4 0.4+0.2 0.125 & = 4 10 25 100 4 10 25 100 + 4 10 4 10 + 2 10 125 1000 = 20 57 aligned