In England, sons of members of the Labor Party vote Labor with probability 0.5,

Question

In England, sons of members of the Labor Party vote Labor with probability 0.5, vote Conservative with probability 0.4, and vote Liberal with probability 0.1. The probabilities for sons of Conservative Party members are 0.7 Conservative, 0.2 Labor, and 0.1 Liberal. For the sons of Liberals the probabilities are 0.2 Conservative, 0.4 Labor, and 0.4 Liberal. Given these statistics, what is the probability that the grandson of a Liberal will vote Labor?

Explanation / Answer

So you know that the grandfather of the voter is Liberal. That means his sons will have probabilities: Conservative: 20% Labor: 40% Liberal: 40% You're asked to find the probability that the Liberal's grandson votes Labor. So if his son is: Conservative son -> Labor grandson: 20% Labor son -> Labor grandson: 50% Liberal son -> Labor grandson: 40% You multiply the probabilities so: .2(.2)=.04 is the probability that his son is conservative and his grandson votes labor .4(.5)=.2 .4(.4)=.16 Add the 3 values: .04+.2+.16=.4=40%

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---