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Chapter 3: Q3.17 (page 98)

In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is (a) the probability that a randomly selected family owns both a dog and a cat? (b) the conditional probability that a randomly selected family owns a dog given that it owns a cat?

Short Answer

Expert verified

P(DogandCat)=0.0792

P(DogICat)=0.264

Step by step solution

01

Given Information of a & b

Given that in a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat

We have to find the probability that a randomly selected family owns both a dog and a cat

Also, find the conditional probability that a randomly selected family owns a dog given that it owns a cat

02

Explanation

03

Explanation-a

a)P(Dog and Cat)=0.36脳0.22

=0.0792

04

Explanation-b

b)P(Dog鈭�cat)=P(Dog and Cat)P(Cat)

P(cat)=0.30given

P(Dog鈭�cat)=0.36脳0.220.30

=0.264

05

Final Answer of a & b

(a) P(Dog and Cat)=0.0792

(b) P(Dog鈭�cat)=0.264

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Most popular questions from this chapter

In Example 3f, suppose that the new evidence is subject to different possible interpretations and in fact shows only that it is 90 percent likely that the criminal possesses the characteristic in question. In this case, how likely would it be that the suspect is guilty (assuming, as before, that he has the characteristic)?

Consider an urn containing 12balls, which 8are white. A sample of size4is to be drawn with replacement (without replacement). What is the conditional probability (in each case) that the first and third balls drawn will be white given that the sample drawn contains exactly3 white balls?

A and B play a series of games. Each game is independently won by A with probability p and by B with probability 1鈭� p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the greater number of total wins is declared the winner of the series.

(a) Find the probability that a total of 4games are played.

(b) Find the probability that A is the winner of the series

What is the probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i,i=2,3,...,12?

(a) An urn containsnwhite and mblack balls. The balls are withdrawn one at a time until only those of the same color are left. Show that with probability n/(n+m), they are all white. Hint: Imagine that the experiment continues until all the balls are removed, and consider the last ball withdrawn.

(b) A pond contains3distinct species of fish, which we will call the Red, Blue, and Greenfish. There are rRed, bBlue, and gGreenfish. Suppose that the fish are removed from the pond in random order. (That is, each selection is equally likely to be any of the remaining fish.) What is the probability that the Redfish are the first species to become extinct in the pond?

Hint: Write PR=PRBG+PRGB, and compute the probabilities on the right by first conditioning on the last species to be removed.
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