A student boasts that he is the luckiest person alive because in a jar of marbles, in which there were two blue marbles and eight red marbles, he drew a blue marble out of the jar on four successive tries (after replacing the original). Skeptical, his friend conducts a simulation using a random number table. The digits 0 and 1 represent a success (drawing a blue marble), and the digits 2 through 9 represent not a success (drawing a red marble). Using the first 10 digits in the first row for the first draw and the next 10 digits in the same row for the second draw, he records the successes.

9 2 6 3 0

7 8 2 4 0

1 9 2 6 7

9 5 4 5 7

5 3 4 9 7

2 3 8 9 4

3 7 7 0 8

7 9 8 6 2

7 6 4 7 1

6 6 4 1 8

7 9 4 4 5

7 8 7 3 5

7 1 5 4 9

4 4 8 4 3

2 6 1 0 4

6 7 3 1 8

0 0 7 0 1

3 4 9 8 6

6 6 7 5 1

9 9 7 2 3

5 9 6 5 4

7 1 9 6 6

2 7 3 8 6

5 0 0 0 4

0 5 3 5 8

9 4 0 3 1

2 9 2 8 1

1 8 5 4 4

5 2 4 2 9

0 6 0 8 0

3 1 5 2 4

4 9 5 8 7

7 6 6 1 2

3 9 7 8 9

1 3 5 3 7

4 8 0 8 6

5 9 4 8 3

6 0 6 8 0

8 4 6 7 5

5 3 0 1 4

0 6 3 4 8

7 6 9 3 8

9 0 7 3 9

5 1 3 9 2

5 5 8 8 7

7 1 0 7 5

0 9 2 0 9

7 9 1 5 7

2 4 4 4 0

3 0 2 4 4

2 8 7 0 3

5 1 7 0 9

9 4 4 5 6

4 8 3 9 6

7 3 7 8 0

0 6 4 3 6

8 6 6 4 1

6 9 2 3 9

5 7 6 6 2

8 0 1 8 1

6 8 1 0 8

8 9 2 6 6

9 4 7 3 0

9 5 7 6 1

7 5 0 2 3

4 8 4 6 4

6 5 5 4 4

9 6 5 8 3

1 8 9 1 1

1 6 3 9 1

Draw 1

9

2

6

3

0

7

8

2

4

0

Number of Successes

Proportion of Success

Draw 1

Red

Red

Red

Red

Blue

Red

Red

Red

Red

Blue

2

0.20 = 20%

Draw 2

1

9

2

6

7

9

5

4

5

7

Number of Successes

Proportion of Success

Draw 2

=___________ %

Part A: Fill in the empty table cells for Draw 2 using the simulation provided.

Part B: What is the proportion of success on Draw 2?

Part C: Discuss collaboratively: What reasonable conclusion can be made about the student's claim that he drew four successive blue marbles out of the jar, knowing that the theoretical probability of doing so is 0.2 0.2 0.2 0.2 = 0.0016 = 0.16%?