The following shows the results of a wine tasting survey of 100 people: 96 like wine A, 93 like wine B, 96 like wine C, 92 like A and B, 91 like B and C, 93 like A and C, 90 like all three wines - Edexcel - A-Level Maths Statistics - Question 5 - 2008 - Paper 1

To find the probability that a randomly selected person does not like any of the three wines, we first find the number of people who like at least one wine:

Total liking at least one wine is:

Total = 100 - (1 + 0 + 2 + 2 + 3 + 1 + 90) = 1.

Thus, the probability is:

$P(none) = \frac{1}{100} = 0.01$

From our Venn diagram, the number of people who like wine A but not wine B is:

Those who like only A = 1.

Thus, the probability is:

$P(A \text{ and not } B) = \frac{1}{100} = 0.01$

From our Venn diagram, the number of people who like any wine except wine C is:

Those who like only A = 1, Those who like only B = 0, Those who like A and B = 2, Those who like only A and C = 3, Those who like only B and C = 1, Those who like all three = 90.

So, the total liking any wine except wine C is:

Total = 1 + 0 + 2 = 3.

Thus, the probability is:

$P(any \text{ except } C) = \frac{3}{100} = 0.03$

From the Venn diagram, those who like exactly two wines are:

Only A and B = 2, Only B and C = 1, Only A and C = 3.

Total liking exactly two wines = 2 + 1 + 3 = 6.

Thus, the probability is:

$P(exactly \; 2) = \frac{6}{100} = 0.06$

Given that a person from the survey likes wine A, we want to find the probability that they also like wine C. We are focusing on those that like A:

From the survey:

• Those who like both A and C = 3 (only A and C) + 90 (all three).
• Total that like A = 1 + 2 + 3 + 90 = 96.

So the probability is:

$P(C \mid A) = \frac{3 + 90}{96} = \frac{93}{96} = 0.96875$