(7) In an affluent suburb of Cleveland, 45% of the adults identify themselves as

Question

(7) In an affluent suburb of Cleveland, 45% of the adults identify themselves as Republicans, 36% identify themselves as Democrats and the rest are undecided. The local Republican Party office randomly selects adults from that suburb and asks him/her about his/her party affiliation. If somebody is a Republican, the chances of him/her getting an invitation to the 2016 Republican National Convention in Cleveland are 90%. For a Democrat, that probability is 20% and for someone undecided, that probability is 70%. Given that a randomly chosen gentleman from that suburb doesn't get an invitation to the 2016 RNC, what is the conditional probability that he is undecided?

Explanation / Answer

Here ,we are given that:

P( republican ) = 0.45, P( democrat ) = 0.36 and P( undecided ) = 1 - 0.45 - 0.36 = 0.19

Also, we are given that:

P( invitation | republican ) = 0.9,
P( invitation | democrat ) = 0.2,
P( invitation | undecided )= 0.7

Now using law of total probability, we get:

P( invitation ) = P( invitation | republican )P( republican ) + P( invitation | democrat )P( democrat ) + P( invitation | undecided )P( undecided )

P( invitation ) = 0.9*0.45 + 0.2*0.36 + 0.7*0.19 = 0.61

Therefore, P( no invitation ) = 1 - 0.61 = 0.39

Now given that there was no invitation, probability that he is undecided is computed using Bayes theorem as:

P( undecided | no invitation ) = P( no invitation | undecided )P( undecided ) / P( no invitation )

P( undecided | no invitation ) = 0.3*0.19 / 0.39 = 0.1462

Therefore 0.1462 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.