Basic Concepts of Probability

Read this section about basic concepts of probability, including spaces, and events. This section discusses set operations using Venn diagrams, including complements, intersections, and unions. Finally, it introduces conditional probability and talks about independent events.

1. S=\{b b, b w, w b, w w\}

3. S=\{r r, r y, r g, y r, y y, y g, g r, g y, g g\}

5. 

a. \{b w, w b\}

b. \{b b\}

7. 

a. \{r r, r g, g r, g g\}

b. \{r r, y y, g g\}

c. Ø

9. 

a. 2 / 4

b. 1 / 4

11. 

a. 4 / 9

b. 3 / 9

c. 0

13. 

a. 0.4

b. 0.5

c. 0.4

15. 

a. 0.21

b. 0.6

c. 0.61

17. 

a. \{b b g, b g b, b g g, g b b, g b g, g g b, g g g\}

b. \{b b b, b b g, b g b, g b b\}

c. \{g g g\}

d. \{b g g, g b g, g g b\}

e. \{g b b, g b g, g g b, g g g\}

19. 

a. 7/8

b. 4/8

c. 1/8

d. 3/8

e. 4/8

21. 

a. 0.25

b. 0.25

c. 0.05

23. 

a. 0.55

b. 0.76

c. 0.19

d. 0.11

25. The relative frequencies for 1 through 6 are 0.16, 0.194, 0.162, 0.164, 0.154 and 0.166. It would appear that the die is not balanced.