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 marking response Yes on the survey, and event A is living in Tokyo. Therefore, the formula was used properly. Now we will check the values of P(AandB) and P(A). Let's look at the given two-way table.
We know that a person lives in Tokyo and marked response Yes on the survey with a probability of 0.049, which is the value of the cell at the intersection of row Yes and the Tokyo column. It corresponds with P(Tokyo and Yes).
P(Tokyo and Yes)= 0.049
Now we will find P(Tokyo), which is the probability that a person lives in Tokyo. As we can see, the value of this marginal relative frequency of the first column is 0.39. The incorrect value in the calculations, 0.356, is the marginal relative frequency of the first row, which corresponds with the marking response Yes on the survey (P(Yes)).
P(Tokyo)= 0.39
With this information, we can calculate P(Yes|Tokyo) correctly.
