Question Video: Using Venn Diagram to Determine the Union of Two Events Mathematics

A survey was conducted on a group of 263 children to determine their favorite superheroes. The results are showed in the Venn diagram. Find 𝑃(Wonder Woman or Batman).

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Video Transcript

A survey was conducted on a group of 263 children to determine their favorite superheroes. The results are showed in the Venn diagram. Find the probability of Wonder Woman or Batman.

Before we begin answering this question, let’s have a quick look at the Venn diagram. The children were asked about the superheroes of Wonder Woman, Superman, or Batman. The values in the Venn diagram indicate the number of children who chose particular superheroes. For example, this value of 14 indicates that 14 children like both Superman and Batman. The value of 75 indicates 75 children chose just Batman.

So when we’re considering the problem to find the probability of Wonder Woman or Batman, it might be really tempting to look at this value nine and think that that would be the answer. However, the value of nine out of 263 children would actually represent the probability of Wonder Woman and Batman.

To find the probability of Wonder Woman or Batman, we need to consider all the children who chose Wonder Woman or Batman. So that’s 64 plus eight plus eight plus nine plus 14 plus 75. Adding these values together would give us the number of children who chose Wonder Woman or Batman. And to give the answer as a probability, we therefore need to divide by the total number of children who were surveyed, and that’s 263. So we get the simplified fraction of 178 over 263.

As a quick check of our arithmetic, if we do add the other value of 85 to 178, we would get the total of 263. As we can’t simplify the fraction 178 over 263 any further, then we can give this as our answer to the probability of Wonder Woman or Batman.