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Taste Testing
Is It Butter?
Hazel is given a piece of bread, spread with either butter or
margarine. She is asked to decide which it is, by guessing
The chance of being right (R), just by guessing, is 1/2.
If two people did the test, the tree diagram would look like
this:
Figure 2 - Tree diagram showing outcome for two
people.
The column headed 'Outcome' tells you how many were right (R)
and wrong (W) each time.
These results are he summarized in Table 2.
Table 2 - Summarized results
for two people.
This shows that if both people guess, it is most likely that
one person will get it right.
Three People
Suppose the test is done by three people. Figure 4 on Page R2
shows only part of the relevant tree diagram.
- Complete it, again assuming that each person
guesses.
- Complete the column headed 'Outcome'. The first
one is done for you.
This time there are 8 (= 2 x 2 x 2 = 23) possible outcomes. The
probability of each outcome is therefore 1/8.
- Complete the column headed 'Probability'.
Use your tree diagram to find:
- Probabifity (all 3 right)
- Probability (exactly 2 right)
- Probability (exactly 1 right)
- Probabifity (no one right)
- Use your answers to complete Table 7 on page R2
which shows the summarized results for three people.
More People
- Is the probability of one person out of two
guessing correctly the same as two people out of four
guessing correctly? Write down what you think.
Figure 5 on page R2 shows the tree diagram when four people
guess. It is not complete.
- Complete it, and the columns headed 'Outcome'
and 'Probability', again assuming
everyone guesses.
Notice there are now 16 (= 2 x 2 x 2 x 2 = 24)
possible outcomes.
Use the tree diagram to find:
- Probability (all 4 right)
- Probability (exactly 3 right)
- Probability (exactly 2 right)
See also if you can answer these questions:
- What is the most likely number of people to guess
correctly?
- Is the probability of two out of four getting it
right the same as the probability of one out of two
getting it right? Use your answers to e and D1c.
- Was your answer to D3a correct?
- *What is the probability of at least one person
being right when four people do the test?
- *What is the probability of at least two people
being wrong when four people do the test?
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