Of registered voters in a certain town, 50% are Democrats,?

40% favor a school ban, and 30% are Democrats who favor a school loan. Suppose that a registered voter is selected at random from the town.

What is the probability that the person is not a Democrat and opposes the school loan?

What is the probability that the person favors the school loan given that he or she is a Democrat?

What is the probability that the person is a Democrat given that her or she favors the school loan?

Of registered voters in a certain town, 50% are Democrats,?

Let%26#039;s write down the probabilities that are known.

P(Democrat) = 0.5

P(Favor) = 0.4

P(Democrat and Favor) = 0.3

We are looking for

P(Not Democrat and Opposes),

P(Favors | Democrat), and

P(Democrat | Favor).

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For the first one it would help to make a Venn diagram. You can find the probabilities in the different sections of the diagram. I can%26#039;t really make the Venn diagram here, but I can hopefully give you the general idea of what goes on with it.

P(Democrat and Favor) = 0.3

P(Democrat and Opposes)

= P(Democrat) - P(Democrat and Favor)

= 0.5 - 0.3

= 0.2

P(Not Democrat and Favors)

= P(Favor) - P(Democrat and Favor)

= 0.4 - 0.3

= 0.1

The only other section that is left in the diagram is P(Not Democrat and Opposes), so that must mean that

P(Not Democrat and Opposes) = 1 - 0.3 - 0.2 - 0.1

= 0.4.

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Using the definition of conditional probability here.

P(Favors | Democrat)

= P(Favors and Democrat)/P(Democrat)

= 0.3/0.5

= 0.6

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P(Democrat | Favors)

= P(Democrat and Favors)/P(Favors)

= 0.3/0.4

= 0.75

edit: Dr D, there is no doubt that that the 30% is P(Democrat and Favor). If it was P(Favor|Democrat), then it would have been worded as you said: 30% OF Democrats favor. You should read more carefully.

And I assume that ban is really loan; possibly the l and o got too close to each other when the problem was written by hand.

Of registered voters in a certain town, 50% are Democrats,?

1.

40%

2.

60%

3.

75%

Of registered voters in a certain town, 50% are Democrats,?

The key to questions like this is to properly define your events.

D = event that a person is a democrat

B = event thatt a person favors the ban

L = event that a person favors the loan

P(D) = 0.5

P(B) = 0.4

P(L int D) = 0.3

RTF: P(Dbar int Lbar)

P(D int Lbar ) = 0.5 - 0.3 = 0.2

RTF: P(L/D) = P(L int D) / P(D)

= 0.3 / 0.5 = 0.6

RTF: P(D/L) = P(L int D) / P(L)

= 0.3 / P(L)

The wording of the question does not allow us any more information. Do you mean to say 30% of democrats who favor the ban. Or 30% of democrats favor the ban. It makes a big difference.

Also the questionn talks about a ban and a loan. Are these two supposed to be the same thing?