Question

For mutually exclusive events Upper R 1?, Upper R 2?, and Upper R 3?, we have ?P(Upper R 1?)equals0.05?,? P(Upper R 2?)equals0.7?, and ?P(Upper R 3?)equals0.25. ?Also, P(Q? | Upper R 1?)equals0.6?, ?P(Q | Upper R 2?)equals0.3?, and? P(Q | Upper R 3?)equals0.8. Find ?P(Upper R 2 ?| Q).

Answer 1

From the given information

P(R2/Q) is given by

According to Baye's theorem

$P(R2/Q)=\frac{P(R_2)*P(Q/R_2)}{P(R_1)*P(Q/R_1)+P(R_2)*P(Q/R_2)+P(R_3)*P(Q/R_3)}$

$=\frac{0.7*0.3}{0.05*0.6+0.7*0.3+0.25*0.8}$

$=\frac{0.21}{0.03+0.21+0.2}$

$=\frac{0.21}{0.44}$

$P(R2/Q)=0.4773$

$P(R2/Q)=0.48$