Probability: Mutually Exclusive Events

COMBINED EVENTS

IN PROBABILITY

Combined events in probability are events that can occur at the same time or in succession.

EXAMPLES:

Rolling Dices to get two sixes

Rolling a dice to get a 2 and flipping a coin to get head

Rolling a dice to get 7 and spinning a spinner to get 3

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MUTUALLY EXCLUSIVE OUTCOMES

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WHEN WE TOSS A COIN, the outcome is either a head or a tail but not both at the same time.

EXAMPLES:

OUTCOMES or EVENTS THAT CANNOT HAPPEN AT THE SAME TIME

What does it mean?

Non-mutually exclusive Events/Outcomes

Rolling a die to get the number 1 and an odd number.

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Scratching your head and turning at the same time.

Multiple Choice

What event or outcomes below are mutually exclusive?

• Rolling a die to get 2 and an even number.

• Tossing a coin to get a tail and closing your eyes.

• Tossing a coin to get a head and rolling a die to get a 6.

• Rolling a die to get a 3 and a 6.

A dice is rolled and a coin is thrown.

a. What are the possible outcomes.

b. What is the probability of throwing a heads and rolling a 5?

​

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MUTUALLY EXCLUSIVE PROBABILITIES

(H, 1)	​(T, 1)
​(H,2)	​(T, 2)
​(H,3)	(T, 3)​
​(H,4)	​(T, 4)
​(H, 5)	​(T, 5)
(H, 6)	(T, 6)

​b)

1 out of 12 outcomes

or, P(H, 5) = 1/12

Multiple Choice

Two coins are thrown.

Sarah's lists out the possible outcomes as: HH, HT, TT

She then estimates the probability of getting two TAILS as P(TT) = 1/3.

Is she correct?

• Yes

• No

Multiple Choice

What is the outcome Sarah forgot to list? (HH, HT, TT, ??)

• H,T

• T,H

• T,T,T

• H,H

Multiple Choice

A, B, C and D all run a race.

What is the total no. of possible outcomes for who wins and who comes second?

• 13

• 14

• 10

• 12

Multiple Choice

What is the probability C wins and D comes second?

• 3/12

• 3/15

• 1/12

• 6/12

Multiple Choice

How many possible combinations of meals are possible?

(M, L), (M, T), …. ?

• 12

• 14

• 16

• 20

Bambam flips a coin and spins the spinner.

What is the probability of getting a tail and an odd number?

P (Tails and Odd Number) =

​Tree Diagram to Estimate Probability