We will check the calculations step by step, starting from verifying the formula for the conditional probability.
P(B|A)=P(AandB)/P(A)
In our case event B is living in London, and event A is marking response No on the survey. Therefore, the formula was used incorrectly. In the denominator should be P(No), not P(London).
P(London|No)=P(No and London)/P(No)
Now we will find the values of P(No and London) and P(London). Let's look at the given two-way table.
We know that a person lives in London and marked response No on the survey with a probability of 0.112, which is the value of the cell at the intersection of row No and column of London. It corresponds with P(No and London).
P(No and London)= 0.112
To find P(No), which is the probability that a person marked response No on the survey, we will use the marginal relative frequency of the second row, which is 0.644.
P(No)= 0.644
With this information we can calculate P(London|No) correctly.
