1. MATH 110 Sec 13.1 Intro to Probability Practice Exercises We are flipping 3 coins and the outcomes are represented by a string of H’s and T’s (HTH, etc.). How many elements are there in the sample space? Express the event “There are more heads than tails” as a set. What is the probability that there are more heads than tails?

2. MATH 110 Sec 13.1 Intro to Probability Practice Exercises We are flipping 3 coins and the outcomes are represented by a string of H’s and T’s (HTH, etc.). How many elements are there in the sample space? Express the event “There are more heads than tails” as a set. What is the probability that there are more heads than tails? By the Fundamental Counting Principle: 2 x 2 x 2 = 8 { HHH, HHT, HTH, THH }

3. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Four cards are drawn from a well-shuffled 52-card deck. What is the probability of drawing a heart?

4. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Four cards are drawn from a well-shuffled 52-card deck. What is the probability of drawing a heart? 13 CLUBS 4 suits (CLUBS, SPADES, HEARTS, DIAMONDS) 13 SPADES 13 HEARTS 13 DIAMONDS

5. What are the odds against drawing a heart? MATH 110 Sec 13.1 Intro to Probability Practice Exercises Four cards are drawn from a well-shuffled 52-card deck. Odds against drawing Heart are 39 : 13 which reduces to 3 : 1. Notice that there are 13 Hearts and 39 non-Hearts

6. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Four cards are drawn from a well-shuffled 52-card deck. What is the probability that all 4 are black?

7. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Four cards are drawn from a well-shuffled 52-card deck. What is the probability that all 4 are black? 26 black cards 26 red cards

8. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Four cards are drawn from a well-shuffled 52-card deck. What is the probability that all 4 are black? From previous picture, there are 26 black cards and 52 cards in all. Because the order the cards are drawn is not important, we count the cards using combinations.

9. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Opinions of residents in a town and surrounding area about a proposed racetrack is given here. SupportOppose Live in town 3325392 Live in area surrounding 4747617 A reporter randomly selects one of these 9081 people to interview. What is the probability that the person is for the track? What are the odds against the person supporting the track?

10. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Opinions of residents in a town and surrounding area about a proposed racetrack is given here. SupportOppose Live in town 3325392 Live in area surrounding 4747617 A reporter randomly selects one of these 9081 people to interview. What is the probability that the person is for the track? What are the odds against the person supporting the track? 1 : 8

11. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the diagram below, what is the probability that it hits the shaded area? (Write final answer as a decimal rounded to 4 decimal places.) 8 in. 6 in. 4 in. 3 in. 2 in. 1 in.

12. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the diagram below, what is the probability that it hits the shaded area? (Write final answer as a decimal rounded to 4 decimal places.) 8 in. 6 in. 4 in. 3 in. 2 in. 1 in. Note: The probability of hitting a region is proportional to the area of that region and the whole diagram. 1 2 2

13. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area? (Write final answer as an integer or simplified fraction.) 21 in. 15 in. 9 in. 6 in.

14. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area? (Write final answer as an integer or simplified fraction.) 21 in. 15 in. 9 in. 6 in. Note: The probability of hitting a region is proportional to the area of that region and the whole diagram.

15. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area? (Write final answer as an integer or simplified fraction.) 21 in. 15 in. 9 in. 6 in. Note: The probability of hitting a region is proportional to the area of that region and the whole diagram. 15 in. Area of the biggest green square is 15 x 15 = 225 225

16. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area? (Write final answer as an integer or simplified fraction.) 21 in. 15 in. 9 in. 6 in. Note: The probability of hitting a region is proportional to the area of that region and the whole diagram. 15 in. Area of the biggest green square is 15 x 15 = 225 9 in. Area of Small blue square is 9 x 9 =81 225 - 81 Subtract blue area b/c it covers up part of the green. 144

17. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area? (Write final answer as an integer or simplified fraction.) 21 in. 15 in. 9 in. 6 in. Note: The probability of hitting a region is proportional to the area of that region and the whole diagram. 15 in. Area of the biggest green square is 15 x 15 = 225 9 in. Area of Small blue square is 9 x 9 =81 225 - 81 Subtract blue area b/c it covers up part of the green. 144 6 in. 36 + 36 The small green square sits on the small blue square and adds back more green. 144 + 36 = 180

18. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area? (Write final answer as an integer or simplified fraction.) 21 in. 15 in. 9 in. 6 in. Note: The probability of hitting a region is proportional to the area of that region and the whole diagram. 15 in. Area of the biggest green square is 15 x 15 = 225 9 in. Area of Small blue square is 9 x 9 =81 225 - 81 Subtract blue area b/c it covers up part of the green. 144 6 in. 36 + 36 The small green square sits on the small blue square and adds back more green. 144 + 36 = 180 So, the total green area is 180 square inches. The total area of the whole figure is 21 x 21 = 441 square inches.

19. MATH 110 Sec 13.1 Intro to Probability Practice Exercises If a dart is thrown and hits somewhere in the figure below which is built from 4 different size squares (2 blue and 2 green), what is the probability that it hits the green area? (Write final answer as an integer or simplified fraction.) 21 in. 15 in. 9 in. 6 in. Note: The probability of hitting a region is proportional to the area of that region and the whole diagram. 15 in. Area of the biggest green square is 15 x 15 = 225 9 in. Area of Small blue square is 9 x 9 =81 225 - 81 Subtract blue area b/c it covers up part of the green. 144 6 in. 36 + 36 The small green square sits on the small blue square and adds back more green. 144 + 36 = 180 So, the total green area is 180 square inches. The total area of the whole figure is 21 x 21 = 441 square inches.

20. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Player 1 & Player 2 play a ame using Spinner A and Spinner B as shown. Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins. Which spinner should Player 1 choose? Assuming that choice of spinner what is the probability that Player 1 wins?

21. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Player 1 & Player 2 play a ame using Spinner A and Spinner B as shown. Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins. Which spinner should Player 1 choose? Assuming that choice of spinner what is the probability that Player 1 wins? List every possible way the 2 spinners could land, then count the # of times each wins.

22. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Player 1 & Player 2 play a ame using Spinner A and Spinner B as shown. Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins. Which spinner should Player 1 choose? Assuming that choice of spinner what is the probability that Player 1 wins? A spin111444999 B spin278278278 Who winsBBBABBAAA List every possible way the 2 spinners could land, then count the # of times each wins.

23. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Player 1 & Player 2 play a ame using Spinner A and Spinner B as shown. Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins. Which spinner should Player 1 choose? Assuming that choice of spinner what is the probability that Player 1 wins? A spin111444999 B spin278278278 Who winsBBBABBAAA B (wins 5 out of 9 times) List every possible way the 2 spinners could land, then count the # of times each wins.

24. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Player 1 & Player 2 play a ame using Spinner A and Spinner B as shown. Player 1 gets to choose one of the spinners, both players spin, and the one getting the larger number wins. Which spinner should Player 1 choose? Assuming that choice of spinner what is the probability that Player 1 wins? A spin111444999 B spin278278278 Who winsBBBABBAAA List every possible way the 2 spinners could land, then count the # of times each wins. B (wins 5 out of 9 times)

25. MATH 110 Sec 13.1 Intro to Probability Practice Exercises Some more detailed solutions and some more problems and solutions can be found here: http://cas.ua.edu/mtlc/UAMath110/Exercises/Sec13-1ExercisesSOL.pdf http://cas.ua.edu/mtlc/UAMath110/Exercises/Sec13-1ExercisesSOL.pdf