Question

Let R1, R2 and R3 be three disjoint events. If Q is an event such that P(R1) = 0.38, P(R2) = 0.31, P(R3) = 0.31, P(Q|R1) = 0.49, P(Q|R2) = 0.32, and P(Q|R3) = 0.3, then P(R1|Q) = , P(R2|Q) = , and P(R3|Q) = .

          Let R1, R2 and R3 be three disjoint events. If Q is an event such that P(R1) = 0.38, P(R2) = 0.31, P(R3) = 0.31, P(Q|R1) = 0.49, P(Q|R2) = 0.32, and P(Q|R3) = 0.3, then P(R1|Q) = , P(R2|Q) = , and P(R3|Q) = .

Added by Mark P.

Finite Mathematics and Calculus with Applications

Margaret L. Lial, Raymond N. Greenwell,… 9th Edition

Chapter 7

Instant Answer

Solved by Expert Haggai Liu

05/26/2020

Step 1

We have: $P(Q \cap R_1) = P(Q|R_1)P(R_1) = 0.49 \cdot 0.38 = 0.1862$ $P(Q \cap R_2) = P(Q|R_2)P(R_2) = 0.32 \cdot 0.31 = 0.0992$ $P(Q \cap R_3) = P(Q|R_3)P(R_3) = 0.3 \cdot 0.31 = 0.093$ Now, we can find the probability of event $Q$ by summing the Show more…

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