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

Answer:

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

$P(A\cup B^{\prime})=\frac{51}{56}$

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;

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

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;

$P(A\cap B^{\prime})=\frac{n(A\cap B^{\prime})}{n(T)}=\frac{12}{56}$

Substituting the values;

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

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

$P(A\cup B^{\prime})=\frac{51}{56}$