A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person cho...

A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

Answer Details

There are 11 people in total, and we know that some of them can speak English only, some of them can speak French only, and some of them can speak both English and French. Let's denote the number of people who can speak both languages as "x". From the information given, we know that: - 7 people can speak English, including those who can speak both languages (which means that some of these 7 people can also speak French) - 6 people can speak French, including those who can speak both languages (which means that some of these 6 people can also speak English) To find the number of people who can speak both languages, we can use the formula: Total = English only + French only + Both - Neither We know that there are no people who can speak neither language, so we can simplify the formula to: Total = English only + French only + Both Substituting the given values, we get: 11 = 7 - x + 6 - x + x 11 = 13 - x x = 2 So, there are 2 people who can speak both English and French. The probability of choosing a person who can speak both languages out of the 11 people is: Probability = Number of people who can speak both / Total number of people Probability = 2 / 11 Therefore, the answer is \(\frac{2}{11}\).