Question

A drawing class was assigned a final project where students had to choose one art medium and one subject. The teacher kept track of the types of projects submitted. A plant An insect Acrylic paint 21 5 Chalk 5 7 Charcoal 7 11 What is the probability that a randomly selected student chose to draw a plant or did not use acrylic paint? Simplify any fractions.

Answer 1

The probability that a randomly selected student chose to draw a plant or did not use acrylic paint is;

`P(A\cup B^(\prime))=(51)/(56)`

Step-by-step explanation:

Given the table in the attached image;

Let A represent the event that a randomly selected student chose to draw a plant, and B' represent the event that a randomly selected student did not use acrylic paint;

`\begin{gathered} P(A)=(n(A))/(n(T))=(33)/(56) \\ P(B^(\prime))=(n(B^(\prime)))/(n(T))=(30)/(56) \end{gathered}`

Recall that the probability that a randomly selected student chose to draw a plant or did not use acrylic paint will be;

`P(A\cup B^(\prime))=P(A)+P(B^(\prime))-P(A\cap B^(\prime))`

The probability of A and B' is;

`P(A\cap B^(\prime))=(n(A\cap B^(\prime)))/(n(T))=(12)/(56)`

Substituting the values;

`\begin{gathered} P(A\cup B^(\prime))=P(A)+P(B^(\prime))-P(A\cap B^(\prime)) \\ P(A\cup B^(\prime))=(33)/(56)+(30)/(56)-(12)/(56)=(63-12)/(56) \\ P(A\cup B^(\prime))=(51)/(56) \end{gathered}`

Therefore, the probability that a randomly selected student chose to draw a plant or did not use acrylic paint is;

`P(A\cup B^(\prime))=(51)/(56)`