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Chapter 3: Q. 3.28 (page 206)

Roll a fair, six-sided die. Let A = a prime number of dots is rolled. Let B = an odd number of dots is rolled. Then A = {2, 3, 5} and B = {1, 3, 5}. Therefore, A AND B = {3, 5}. A OR B = {1, 2, 3, 5}. The sample space for rolling a fair die is S = {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.

Short Answer

Expert verified

The Venn diagram is as follows:

Step by step solution

01

Given Information

Roll a fair, six-sided die. Let A= a prime number of dots is rolled. Let B= an odd number of dots is rolled. Then A={2,3,5}and B={1,3,5}. Therefore, AANDB={3,5}and ARB={1,2,3,5}. The sample space for rolling a fair die is S={1,2,3,4,5,6}.

02

Calculation

We have

Sample space for rolling a fair die is S={1,2,3,4,5,6}

Event A= a prime number of dots is rolled

Event B= an odd number of dots is rolled.

A={2,3,5}B={1,3,5}AANDB={3,5}AORB={1,2,3,5}

Thus, Venn diagram is as follows

03

Conclusion

Hence, the Venn diagram representing the situation is sketched.

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Most popular questions from this chapter

A box is filled with several party favors. It contains 12

hats, 15 noisemakers, ten finger traps, and five bags of confetti.

Let H = the event of getting a hat.

Let N = the event of getting a noisemaker.

Let F = the event of getting a finger trap.

Let C = the event of getting a bag of confetti.

Find P(F).

You have a fair, well-shuffled deck of 52 cards. It consists of four suits. The suits are clubs, diamonds, hearts and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit. Three cards are picked at random.

a. Suppose you know that the picked cards are Q of spades, K of hearts and Q of spades. Can you decide if the sampling was with or without replacement?

b. Suppose you know that the picked cards are Q of spades, K of hearts, and J of spades. Can you decide if the sampling was with or without replacement?

In words, explain what it means to pick one person from the study who is “Japanese American AND smokes 21to30 cigarettes per day.” Also, find the probability.

Write the symbols for the probability that a player is an outfielder or is a great hitter.

Use the following information to answer the next six exercises. There are 23countries in North America, 12countries in

South America, 47countries in Europe, 44countries in Asia, 54countries in Africa, and 14in Oceania (Pacific Ocean

region).

Let A = the event that a country is in Asia.

Let E = the event that a country is in Europe.

Let F = the event that a country is in Africa.

Let N = the event that a country is in North America.

Let O = the event that a country is in Oceania.

Let S = the event that a country is in South America.

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