Answer to Question #202665 in Statistics and Probability for umidu

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

$N(B)=5, N(M)=10, N(F)=8,$

$N(M\cap F)=6$

$N(U)=25$

a)

$$P(B\cup M)=\dfrac{5+10}{25}=\dfrac{3}{5}$$

b)

$$P( M)=\dfrac{10}{25}=\dfrac{2}{5}$$

$$P(F)=\dfrac{8}{25}$$

$$P(M)P(F)=\dfrac{2}{5}(\dfrac{8}{25})=\dfrac{16}{125}$$

$$P(M\cap F)=\dfrac{6}{25}\not=\dfrac{16}{125}=P(M)P(F)$$

The events “The randomly selected customer purchased Milk” and “The randomly selected customer purchased Fruits” are not independent.