probabilty please help

Q1. [CLO2, PLO2] (2 marks) Suppose that a robot is in front of a door, which is either open (with 60% probability) or closed (with 40% probability). Suppose that the sensor installed in the robot determines that the measurement probability of an opened door, P(z,/open), is 0.7 and that of a closed door is 0.2. (a) Find out the total measurement probability P(z1). (b) Find out the probability of an opened door given the measurement. Ans P(z, | open) = 0.7 P(z, | open) = 0.2 P(open) = 0.6, P(open) 0.4 (a) P(z,) P(z, |open) p(open) P(z, |open) p(open) P(z,) (0.7)(0.6) (0.2)(0.4) 0.5 P(open | z,) P(z, | open) P(open) (b) P(Z, ) P(open | z,) (0.7)(0.6) 0.42 0.5 0.5 0.84 Now, suppose that the sensor installed in the robot gives a second set of measurements for the open door to be 0.5 and that of a closed door to be 0.6. (c) Find out the total probability for the second measurement. (d) Find out the probability of an opened door given the two measurements