Question

1.    The manager of a supermarket collected the data of 25 customers on a certain date. Out of them 5 purchased Biscuits, 10 purchased Milk, 8 purchased Fruits, 6 purchased both Milk and Fruits.

Let B represents the randomly selected customer purchased Biscuits, M represents the randomly selected customer purchased Milk and F represents the randomly selected customer purchased Fruits.

Represent the given information in a Venn diagram. Use that Venn diagram to answer the following questions.

a)       Find the probability that a randomly selected customer either purchased Biscuits or Milk.

b)      Show that the events “The randomly selected customer purchased Milk” and “The randomly selected customer purchased Fruits” are independent.

Answer 1

The answer is ambiguous. Consider, for example, two possible diagrams on the picture.

$ase\,\,1.\\a:\\P\left( B\cup M \right) =\frac{10+5}{25}=0.6\\Case\,\,2.\\a:\\P\left( B\cup M \right) =\frac{10}{25}=0.4\\b\,\,is\,\,incorrect:\\P\left( M\cap F \right) =\frac{6}{25}\\P\left( M \right) P\left( F \right) =\frac{10}{25}\cdot \frac{8}{25}=\frac{16}{125}$