Addition Rule with Non-Mutually Exclusive Events

Addition Rule, probability of this or that

By Kelly Spring

​Example: Probability draw a 4 from a deck of cards or draw a Jack.

Both cannot occur at same time

​Example: Probability draw a Heart from a deck of cards or draw a King.

Both can occur at same time

Remember, probabilities can be expressed as a fraction, decimal, or percent.

Multiple Choice

Ralph and Dan are the star soccer players on the team.

How would you calculate the probability that Ralph or Dan will play in a tournament?

• P(Ralph plays)

  + P(Dan plays)

• P(Ralph plays)

  + P(Dan plays)

  - P(Ralph & Dan play)

• P(Ralph plays)

  + P(Dan plays)

  x P(Ralph & Dan play)

Multiple Choice

There is a 50% chance that a star player, Ralph, will play in the tournament.

The probability that another star player, Dan, will play is 0.48.

The probability that both Ralph and Dan will play in the tournament is 0.25.

What is the probability that either Ralph or Dan will play in the tournament?

(HINT: Convert "50% chance" to a decimal.)

• 1.23

• 0.48

• 0.98

• 0.73

Multiple Choice

There are 50 students. Some students take a foreign language course.

16 of the students take French.

21 of the students take Spanish.

7 of the students take French and Spanish.

What is the probability that a student takes FRENCH or SPANISH?

• 40%

• 30%

• 50%

• 60%

Multiple Choice

How many adults purchased tickets in advance?

• 48

• 100

• 40

• 62

Multiple Choice

How many total children attended the concert?

• 148

• 102

• 110

• 140

Multiple Choice

What is the probability that a randomly selected person attending the concert is an ADULT?

• 59.2%

• 75.2%

• 66.2%

• 43.2%

Multiple Choice

What is the probability that a randomly selected person attending the concert PURCHASED THE TICKET IN ADVANCE?

• 56%

• 76%

• 66%

• 86%

Multiple Choice

What is the probability that a randomly selected person attending the concert is an ADULT and PURCHASED THE TICKET IN ADVANCE?

• 40%

• 30%

• 20%

• 50%

Multiple Choice

What is the probability that a randomly selected person attending the concert is an ADULT or has PURCHASED THE TICKET IN ADVANCE?

• 75.2%

• 68.2%

• 58.2%

• 65.2%

Multiple Choice

A total of 50 students play either soccer or lacrosse.

20 girls play lacrosse.

20 boys play either soccer or lacrosse.

20 students play soccer.

What is the probability that a student PLAYS SOCCER or IS A GIRL?

• 40%

• 60%

• 20%

• 80%