Help

- Watch
- - Try This
  - Differences Between Experiment and Theory
  - Increasing the Number of Trials
  - Further Examples
  - Alternative Format
- Review
- - Question 1
  - Question 2
  - Question 3
- Practise
- - Exercises
  - Answers and Solutions
- Question Descriptions

Try This Problem Revisited

Spinner 1

A spinner split into four sections labelled with numbers. Sections 1 and 3 make up two-tenths and Sections 2 and 4 make up three-tenths of the spinner.

Spinner 2

A spinner split into five sections labelled with numbers. Sections 1, 3, and 5 make up one-tenth of the spinner. Section 2 makes up four-tenths, and Section 4 makes up three-tenths of the spinner.

The outcomes of my \(10\) spins are: \(4, ~3, ~2, ~4, ~4, ~1, ~4, ~2, ~3, ~2\)
Can you guess which spinner I used?

Spinner 1 \[\class{timed add4-hl2 remove5-hl2}{1,1},~\class{timed add5-hl2 remove6-hl2}{2,2,2},~\class{timed add4-hl2 remove5-hl2}{3,3},~\class{timed add5-hl2 remove6-hl2}{4,4,4}\]
Spinner 2
\[1,~ 2,2,2,2,~3,~4,4,4,~ 5\]

Try This Problem Revisited Continued

Spinner 1

A spinner split into four sections labelled with numbers. Sections 1 and 3 make up two-tenths and Sections 2 and 4 make up three-tenths of the spinner.

Spinner 2

A spinner split into five sections labelled with numbers. Sections 1, 3, and 5 make up one-tenth of the spinner. Section 2 makes up four-tenths, and Section 4 makes up three-tenths of the spinner.

Is there a way to change this game to make you more confident in your guess?

Solution

	Actual Results
1	\(12\)
2	\(46\)
3	\(11\)
4	\(25\)
5	\(6\)

	Expected Results (Spinner 1)	Expected Results (Spinner 2)
1	\(20\)	\(10\)
2	\(30\)	\(40\)
3	\(20\)	\(10\)
4	\(30\)	\(30\)
5	\(0\)	\(10\)

Example 1

Perform the following activities:

Toss a fair coin \(10\) times and calculate the probability of tossing a head based on this data.
Toss a fair coin \(50\) times and calculate the probability of tossing a head based on this data.
Combine your data with as many people as possible to increase the total number of trials. Calculate the probability of tossing a head based on this combined data.

Explore This 1

Example 1 Continued

Do you notice anything when you compare the three experimental probabilities to each other and to the theoretical probability of tossing a head?

10 Tosses

Heads	Tails
\(7\)	\(3\)

\(70\%\)

50 Tosses

Heads	Tails
\(22\)	\(28\)

\(44\%\)

1000 Tosses

Heads	Tails
\(486\)	\(514\)

\(48.6\%\)

None of the experimental probabilities match the theoretical probability of tossing heads.
The experimental probabilities got closer to \(50\%\) as the number of tosses increased.

Increasing the number of tosses does not guarantee an experimental probability that is closer to the theoretical probability.
Experimental probabilities between \(48\%\) and \(52\%\) were much more common for \(1000\) tosses than for \(10\) tosses.

Check Your Understanding 1

Paused Finished

Slide /

Slide Notes

Glossary

All Slides

Navigation