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The number of votes for each of 2 candidates in a local election is shown in the table below. The electorate is divided into 3 different wards.  Ward 1 Ward 2 Ward 3Candidate A 152 84 122Candidate B 100 64 110What is the probability that someone lives in Ward 3 given that they voted for candidate B?

Question

The number of votes for each of 2 candidates in a local election is shown in the table below. The electorate is divided into 3 different wards.  Ward 1 Ward 2 Ward 3Candidate A 152 84 122Candidate B 100 64 110What is the probability that someone lives in Ward 3 given that they voted for candidate B?

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Solution

To find the probability that someone lives in Ward 3 given that they voted for candidate B, we need to use the formula for conditional probability.

Step 1: Find the total number of votes for candidate B.

Candidate B received 100 votes from Ward 1, 64 votes from Ward 2, and 110 votes from Ward 3. So, the total number of votes for candidate B is 100 + 64 + 110 = 274 votes.

Step 2: Find the number of votes for candidate B in Ward 3.

Candidate B received 110 votes from Ward 3.

Step 3: Calculate the conditional probability.

The probability that someone lives in Ward 3 given that they voted for candidate B is the number of votes for candidate B in Ward 3 divided by the total number of votes for candidate B.

So, the probability is 110 / 274 = 0.401 (rounded to three decimal places).

Therefore, the probability that someone lives in Ward 3 given that they voted for candidate B is approximately 0.401 or 40.1%.

This problem has been solved

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