Choice Or Chance Statistics In Your World 
Student Notes
Teachers Notes
Can We Go Further?
 
Comparing Probabilities
 
Were You Right?
 
Changing the Chance
 

More People

*Can We Go Further?
Figure 5 is rather large and unwieldy.

The results are shown in Table 3.

Number right Possible ways Number of ways Probability
0 WWWW 1 1/16
1 RWWW, WRWWW, WWRW, WWWR 4 4/16
2 WWRR, WRRW, RRWW, WRWR, RWRW, RWWR 6 6/16
3 WRRR, RWRR, RRWR, RRRW 4 4/16
4 RRRR 1 1/16
Total   16 1

Table 3 - Summarized results for four people.

Table 4 shows the number of ways two, three and four people can guess correctly. The figures come from Tables 2, 7 and 3.

  Number guessing
1 2 3 4 5
Number of
right
answers		 0   1 1 1  
1   2 3 4  
2   1 3 6  
3     1 4  
4       1  
5          
Total number
of ways		     4 8 16  

Table 4 Summarized results for different numbers of people.

  1. Make a copy of Table 4.
  2. Complete column 1, when one person guesses.
  3. Fill in 'Total number of ways' for five people.
  4. Fill in column 5.
  5. Draw an outline for a table similar to Table 3 to show the possible outcomes when five people do the test.
  6. Use the numbers you put in Table 4 to complete the column headed 'Number of ways'.
  7. Now see if you can find all the different 'Possible ways' to complete that column, and complete the column headed 'Probability'.

Use your completed table to find for five people:

  1. Probability (all right)
  2. Probability (exactly 4 right)
  3. The most likely number of people that got it right
  4. Probability (at least 1 got it right)
  5. *Probability (at least 2 got it wrong).

 

Comparing Probabilities
We have seen that when the probability, of success is 1/2 and there are two people doing the test, the probability that just one gets it right is 1/2.

When there are four people, the probability that two get it right is 3/8.

So doubling the number of people changes the probability, but does not double it. In fact, it makes it smaller.

When there are five people, the probability of exactly four getting it right is 5/32.

  1. Do you think the probability of exactly 8 people out of 10 getting it right will be the same as, more than, or less than 5/32? Write down which you think.
  2. *It is not easy to work out what the probability of exactly 8 out of 10 getting it right is, but if you use the ideas in E1 you may be able to work it out. Try and see.
  3. *Was your answer to E2a right?

 

Were You Right?
If you haven't worked it out, ask your teacher for the probability that 8 out of 10 people guess correctly. Remember this probability can be achieved by chance alone.

Think what the statement '8 out of 10' could mean.
It could mean 8 out of every 10.
It could mean 8 out of only one sample of 10.

  1. Can you think of any other possible meanings for 8 out of 10? If so, write them down.
  2. Look back at the answer you gave to the very first question of Section Al. Do you wish to change that answer now?
  3. Describe the circumstances in which you feel you would be prepared to accept the claim that '8 out of 10 owners said their cat preferred Whiskas' as real evidence of Whiskas being the most popular cat food.

 

Changing the Chance
Suppose there were five pieces of bread with margarine on and only one with butter.

  1. What is the chance of identifying the piece with butter by guesswork?
  2. Find the Probability (exactly 1 person right out of 2) in this case. Compare this answer with the one you gave in D1c.
  3. Write down what you notice.
  4. Find the Probability (exactly 2 people right out of 4) in this case. Compare this answer with the one you gave in D3c.
  5. Write down what you notice.

Suppose the experiment in Section A1 involved one bowl of Whiskas and five other bowls of different cat food.

  1. Would you be more convinced of the advertiser's claim? Give reasons.

 

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