Answer:
3. P(R1|Q) = 3/19 ≈ 0.16
Step-by-step explanation:
The desired probability is the ratio of P(Q·R1) to P(Q). The probability P(Q) is not given, but there is sufficient information to find it.
P(Q·R1) = P(Q|R1)·P(R1) = 0.40·0.15 = 0.06
P(Q·R2) = P(Q|R2)·P(R2) = 0.20·0.55 = 0.11
P(Q·R3) = P(Q|R3)·P(R3) = 0.70·0.30 = 0.21
Since R1 and R2 and R3 are mutually exclusive and have a joint probability of 1, this means ...
P(Q) = P(Q·R1) +P(Q·R2) +P(Q·R3) = 0.06 +0.11 +0.21 = 0.38
Then the desired probability is ...
P(R1|Q) = P(Q·R1)/P(Q) = 0.06/0.38
P(R1|Q) = 3/19 ≈ 0.16
