Probability of Multiple Events

EQ: What is the difference between independent and dependent events? How do you calculate

probability of multiple events?

INDEPENDENT VS. DEPENDENT EVENTS

• Independent: the occurrence of one event does NOT affect how the second event will turn out

• Dependent: the occurrence of one event CHANGES the probability of the second event

Ex 1) Roll a dice, then roll it again

Ex 2) Take a marble out of a bag, then take another one out

Ex 3) Flip a coin, then roll a dice

Ex 4) Pick a card out of a deck, then pick another one

INDEPENDENT

DEPENDENT

INDEPENDENT

DEPENDENT

• Mutually Exclusive Events: events that cannot happen simultaneously (“at the same time”)

Ex 1) Roll an even number, roll an odd number (one dice)

Ex 2) Pick a shirt that is red, pick a shirt with long sleeves

MUTUALLY EXCLUSIVE

Not Mutually Exclusive

U symbol for OR

“probability that A or B will happen”

P(A U B) = P(A) + P(B)

**Only works for mutually exclusive events**

symbol for AND

“probability that A AND B will happen”

P(A B) = P(A) P(B)∙

**Only works for independent events**

Bottom Line:

OR ( U ) = ADD

AND ( )= MULTIPLY

1. P(made shot): _________ P(passes the can): __________

• 2. Are making the shot and missing the shot mutually exclusive? Why/why not?

• 3. Draw a Venn diagram comparing “making the shot” , “missing the shot” , and “passing the can”:

• 4. What is the probability that this student makes the shot OR the ball passes the can?

• 5. Are the two events (Student A shooting, Student B shooting) independent? Why/why not?

• 6. Are the events (Student A makes it, student B makes it) mutually exclusive? Why/why not?

• 7. Draw a Venn diagram comparing of Student A making/missing a shot to Student B making/missing a shot

• 8. What is the probability of Student A OR Student B making the shot?

• 9. What is the probability of Student A AND Student B making the shot?

1. Assume that Q and R are independent & mutually exclusive events.

1 2,8 5

P Q P R

𝑃 (𝑄∩𝑅 )=¿ 𝑃 (𝑄∪𝑅 )=¿

• 2. There are a total of 30 students taking math and/or science. If you there are 18 students taking a math, and 21 students are taking a science, how many must be taking both?

• 3. Of the 195 students in the senior class, 104 study Spanish and 86 study French, with 12 studying both Spanish and French. What is the theoretical probability that a student chosen at random is studying Spanish, but not French?

• 4. A bucket contains 15 blue pens, 35 black pens, and 40 red pens. You pick one pen at random. Find each theoretical probability.

a. P(blue pen or red pen)

b. P(black pen or not a red pen)

c. P(black pen and a blue pen)

5. Exactly 62% of the students in your school are under 17 years old. In addition, 4% of the students are over 18. What is the probability that a student chosen at random is under 17 or over 18?

6. What is the probability that you will grab a shape out of the bucket to the right that is black OR has 5 points?

7. What is the probability that you will grab a heart OR a gray shape?

8. What is the probability that you will grab a shape that is black AND a heart?

9. You have a drawer with five pairs of white socks, three pairs of black socks, and one pair of red socks. You choose one pair of socks at random each morning, starting on Monday. You do not put the socks you choose back in the drawer. Find the probability of each event.

a. You select black socks on Monday and white socks on Tuesday.

b. You select red socks on Monday and black socks on Tuesday.

c. You select white socks on Monday and Tuesday.