Joe is about to take one of three tests: Quantum Field Theory (QFT), General Rel

Question

Joe is about to take one of three tests: Quantum Field Theory (QFT), General Relativity (GR), or Writing in Terminology That's Fun (WTF). Joe has a 20% chance of sitting next to his (much smarter) friend Jan. If he sits next to Jan. he has a 45% chance of passing QFT which he will have a 25% chance of taking; a 55% chance of passing GR, which he will have a 50% chance of taking; and an 80% chance of passing WTF, which he will have a 25% chance of taking. If he does not sit next to Jan, he has a 30% chance of passing QFT, which he will have a 20% chance of taking; a 40% chance of passing GR, which he will have a 50% chance of taking; and a 75% chance of passing WTF, which he will have a 30% chance of taking. What is the probability that Joe passes the test?

Explanation / Answer

joe passess the test =P(sit next to Jan and passess)+P(does not set next to Jan and passess)

=0.2*(0.45*0.25+0.55*0.5+0.8*0.25)+0.8*(0.3*0.2+0.4*0.5+0.75*0.3)=0.5055

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