SOLUTION: For mutually exclusive events X1, X2, and X3, let P(X1) = .22, P(X2) = .35 and P(X3) = .43. Also, P(Y | Y1) = .40 P(Y|X2) = .30 and P(Y|X3) = .60. Find P(X3|Y) A) . 20 B) . 57

Question 231683: For mutually exclusive events X1, X2, and X3, let P(X1) = .22, P(X2) = .35 and P(X3) = .43. Also, P(Y | Y1) = .40 P(Y|X2) = .30 and P(Y|X3) = .60. Find P(X3|Y)
A) . 20 B) . 57 C) . 38 D) . 23
This theorem is so complicated for me that I dont know where to begin.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For mutually exclusive events X1, X2, and X3,
let P(X1) = .22, P(X2) = .35 and P(X3) = .43.
Also, P(Y | X1) = .40 P(Y|X2) = .30 and P(Y|X3) = .60.
Find P(X3|Y)
---
P(X3 | Y) = P(X3 and Y)/P(Y)
----------------------------------
You are told P(Y | X3) = 0.6
So P(Y and X3)/P(X3) = 0.6
and P(Y and X3)/0.43 = 0.6
So, P(Y and X3) = 0.43*0.6 = 0.258
------------------------------------
Using that result you have:
P(X3 | Y) = 0.258/P(Y)
-----------------------
But P(Y) = P(Y|X1) + P(Y|X2) + P(Y|X3) = 0.4 + 0.3 + 0.6 = 1.3
=============================================================
Final Answer: P(X3 |Y) = 0.258/1.3 = 0.198
Round you be 0.20
which is answer "A"
---
Cheers,
Stan H.
A) . 20 B) . 57 C) . 38 D) . 23

RELATED QUESTIONS
X and Y are independent, X ~ P(λ1), Y ~ P(λ2). Given probabilities P(X1 > 0) = 0.58,... (answered by parmen)

Let P(x) be the probability function of a discrete random variable x which assumes the... (answered by stanbon)

The following maximum problem is in standard form. Introduce slack variables and set up... (answered by solver91311)

The following maximum problem is in standard form. Introduce slack variables and set up... (answered by Edwin McCravy)

Graph p(x)= (-)x3 - (3)x2 +... (answered by checkley71)

P(C)= 0.2 P(B)= 0.3 And Events are Mutually Exclusive.. Find... (answered by tenkun)

Graph the equation by finding the x and y intercepts. - 4x + 3y = -12 x1 / y1 x2... (answered by Alan3354,MathLover1,solver91311)

Find P and Q if X1 = 14, n1 = 20, X2 = 23, n2 =... (answered by ikleyn)

factor and name the roots of... (answered by MathLover1)