How to Solve Venn Diagrams and the Addition Rule?

In a Venn diagram, this might look like this:

(color{blue}{P(A∪B)=P(A)+P(B)})

Venn Diagrams and the Addition Rule, Example 1:

In a group of (103) students, (32) are freshmen and (46) are sophomores. Find the probability that a student picked from this group at random is either a freshman or sophomore.

First, find the probability of freshman and sophomore:

(P( freshman)=frac{32}{103})

(P( sophomores)=frac{46}{103})

Then, use this formula to find the probability of freshman or sophomore: (color{blue}{P (A or B)=P (A)+P (B)})

(P( freshman or sophomore)=frac{32}{103}+frac{46}{103}=frac{32+46}{103}=frac{78}{103}).

Venn Diagrams and the Addition Rule, Example 2:

In a group of (114) students, (41) are juniors, (50) are male, and (23) are male juniors. Find the probability that a student picked from this group at random is either a junior or male.

First, find the probability of juniors, male and male juniors:

(P ( juniors)=frac{41}{114})

(P ( male)=frac{50}{114})

(P (male juniors)=frac{23}{114})

Then, use this formula to find the probability junior or male: (color{blue}{P (A or B)=P (A)+P (B)−P (A and B)})

(P( junior or male )=frac{41}{114}+frac{50}{114}-frac{23}{114}=frac{(41+50)-23}{114}=frac{91-23}{114}=frac{68}{114})

Exercises for Venn Diagrams and the Addition Rule

1. We have to draw a card from a well-shuffled (52)-card deck. So what is the chance of getting a diamond or a face card?
2. For two events (A) and (B), (P(A)= frac{3}{5}), (P(B) = frac{3}{4}), and (P(A∪B) = frac{5}{6}). Find the probability of (A∩B).
3. A glass jar consists of (3) green,(2) red, (3) blue and (4) yellow marbles. If a marble is randomly selected from a jar, how likely is it to be yellow or green?
4. A day of the week is chosen at random. What is the probability of choosing on Sunday or Monday?

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1. (color{blue}{frac{11}{26}})
2. (color{blue}{frac{31}{60}})
3. (color{blue}{frac{7}{12}})
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