MULTIPLE CHOICE TEST Wjfnthdutk? a.)vnb b.)hfg c.)yrt d.)lpo

1. 1. • MULTIPLE CHOICE TEST • Wjfnthdutk? a.)vnb b.)hfg c.)yrt d.)lpo • Tudngimktpl? a.)vnb b.)hfg c.)yrt d.)lpo • Nbdfrrfewvxc? a.)vnb b.)hfg c.)yrt d.)lpo • Cuytgfdsaq? a.)vnb b.)hfg c.)yrt d.)lpo • Bhnmopmkjhy? a.)vnb b.)hfg c.)yrt d.)lpo A multiple choice test has 5 questions. There are 4 choices for each answer. If you GUESS each answer, what is the probability that you get AT LEAST one right answer?

2. MULTIPLE CHOICE TEST • Wjfnthdutk? a.)vnb b.)hfg c.)yrt d.)lpo • Tudngimktpl? a.)vnb b.)hfg c.)yrt d.)lpo • Nbdfrrfewvxc? a.)vnb b.)hfg c.)yrt d.)lpo • Cuytgfdsaq? a.)vnb b.)hfg c.)yrt d.)lpo • Bhnmopmkjhy? a.)vnb b.)hfg c.)yrt d.)lpo A multiple choice test has 5 questions. There are 4 choices for each answer. If you GUESS each answer, what is the probability that you get AT LEAST one right answer? The event that “you get AT LEAST one right answer” = the event that “you do NOT get all wrong answers”.

3. MULTIPLE CHOICE TEST • Wjfnthdutk? a.)vnb b.)hfg c.)yrt d.)lpo • Tudngimktpl? a.)vnb b.)hfg c.)yrt d.)lpo • Nbdfrrfewvxc? a.)vnb b.)hfg c.)yrt d.)lpo • Cuytgfdsaq? a.)vnb b.)hfg c.)yrt d.)lpo • Bhnmopmkjhy? a.)vnb b.)hfg c.)yrt d.)lpo in how many ways can you answer this question incorrectly? A multiple choice test has 5 questions. There are 4 choices for each answer. # ways of answering all of the questions = 4 x 4 x 4 x 4 x 4 = 1024 If you GUESS each answer, what is the probability that you get AT LEAST one right answer? The event that “you get AT LEAST one right answer” = the event that “you do NOT get all wrong answers”. # ways of answering each question incorrectly = 3 x 3 x 3 x 3 x 3 = 243 P ( you get all wrong answers ) = 243 1024

4. MULTIPLE CHOICE TEST • Wjfnthdutk? a.)vnb b.)hfg c.)yrt d.)lpo • Tudngimktpl? a.)vnb b.)hfg c.)yrt d.)lpo • Nbdfrrfewvxc? a.)vnb b.)hfg c.)yrt d.)lpo • Cuytgfdsaq? a.)vnb b.)hfg c.)yrt d.)lpo • Bhnmopmkjhy? a.)vnb b.)hfg c.)yrt d.)lpo A multiple choice test has 5 questions. There are 4 choices for each answer. # ways of answering all of the questions = 4 x 4 x 4 x 4 x 4 = 1024 If you GUESS each answer, what is the probability that you get AT LEAST one right answer? • 1024 • 243 • 781 The event that “you get AT LEAST one right answer” = the event that “you do NOT get all wrong answers”. # ways of answering each question incorrectly = 3 x 3 x 3 x 3 x 3 = 243 P ( you get all wrong answers ) = 243 1024 P ( you do NOT get all wrong answers ) = 781 1024

5. 2. Roll 3 dice. What is the probability that: 1.) All the numbers are EVEN? 2.) AT LEAST one number is ODD? 3.) All the numbers are different? 4.) AT LEAST two are the same? 5.) No die lands on the number “4”? 6.) AT LEAST one die lands on the number “4”?

6. 2. Roll 3 dice. What is the probability that: 1.) All the numbers are EVEN? 2.) AT LEAST one number is ODD? 3.) All the numbers are different? 4.) AT LEAST two are the same? 5.) No die lands on the number “4”? 6.) AT LEAST one die lands on the number “4”? there are 3 even numbers on the blue die (2,4,6) there are 3 even numbers on the red die (2,4,6) there are 3 even numbers on the green die (2,4,6)

7. 2. Roll 3 dice. What is the probability that: 1.) All the numbers are EVEN? 2.) AT LEAST one number is ODD? P( NOT all even ) = 3.) All the numbers are different? 4.) AT LEAST two are the same? 5.) No die lands on the number “4”? 6.) AT LEAST one die lands on the number “4”?

8. 2. Roll 3 dice. What is the probability that: 1.) All the numbers are EVEN? 2.) AT LEAST one number is ODD? P( NOT all even ) = 3.) All the numbers are different? 4.) AT LEAST two are the same? 5.) No die lands on the number “4”? 6.) AT LEAST one die lands on the number “4”?

9. 2. Roll 3 dice. What is the probability that: 1.) All the numbers are EVEN? 2.) AT LEAST one number is ODD? P( NOT all even ) = 3.) All the numbers are different? 4.) AT LEAST two are the same? P ( NOT all different ) = 5.) No die lands on the number “4”? 6.) AT LEAST one die lands on the number “4”?

10. 2. Roll 3 dice. What is the probability that: 1.) All the numbers are EVEN? 2.) AT LEAST one number is ODD? P( NOT all even ) = 3.) All the numbers are different? 4.) AT LEAST two are the same? P ( NOT all different ) = 5.) No die lands on the number “4”? 6.) AT LEAST one die lands on the number “4”?

11. 2. Roll 3 dice. What is the probability that: 1.) All the numbers are EVEN? 2.) AT LEAST one number is ODD? P( NOT all even ) = 3.) All the numbers are different? 4.) AT LEAST two are the same? P ( NOT all different ) = 5.) No die lands on the number “4”? 6.) AT LEAST one die lands on the number “4”? P ( NOT “no fours”) =

12. 3. Draw 2 marbles without replacement. What is the probability that: 1.) they are both red? 2.) at least one is green? 3.) they are the same color?

13. 3. Draw 2 marbles without replacement. What is the probability that: 1.) they are both red? 2.) at least one is green? 3.) they are the same color? red 6/56 2/7 red 5/7 green 15/56 3/8 5/8 15/56 red 3/7 green 4/7 green 20/56

14. 3. Draw 2 marbles without replacement. What is the probability that: 1.) they are both red? 6/56 2.) at least one is green? 3.) they are the same color? red 6/56 2/7 red 5/7 green 15/56 3/8 5/8 15/56 red 3/7 green 4/7 green 20/56

15. 3. Draw 2 marbles without replacement. What is the probability that: 1.) they are both red? 6/56 2.) at least one is green? 1 - 6/56 = 50/56 3.) they are the same color? red 6/56 2/7 red 5/7 green 15/56 3/8 5/8 15/56 red 3/7 green 4/7 green 20/56

16. 3. Draw 2 marbles without replacement. What is the probability that: 1.) they are both red? 6/56 2.) at least one is green? 1 - 6/56 = 50/56 3.) they are the same color? 26/56 red 6/56 2/7 red 5/7 green 15/56 3/8 5/8 15/56 red 3/7 green 4/7 green 20/56