Download Compound Events

Compound Events
Unit 4: Chance of Winning
What is a compound event?
• A compound event combines two or more
events, using the word and or the word or.
• Example: Find the probability of red and
yellow when spinning a spinner.
• There are four types of compound events:
mutually exclusive events, mutually
inclusive events, independent events, and
dependent events.
What are mutually exclusive
events?
• Mutually exclusive events have no
common outcomes.
• If A and B are mutually exclusive events,
then P(A or B)= P(A) + P(B).
Example
• You randomly choose a card from a
standard deck of 52 playing cards.
Find the probability that you choose a
Queen or an Ace.
• P(Queen or Ace) = P(Queen) + P(Ace) =
4
4
8
2



52 52 52 13
What are mutually inclusive
events?
• Mutually inclusive events have at least one
common outcome.
• If A and B are mutually inclusive events,
then P(A or B)= P(A) + P(B) – P(A and B).
Example
• You randomly choose a card from a standard deck of 52
playing cards.
Find the probability that you choose a King or an club.
• Because there is a King of clubs, these are mutually
inclusive events.
• P(King or club) = P(King) + P(club) – P(King and club) =
4 13 1 16 4
 


52 52 52 52 13
What are independent events?
• Independent events are two events where
the occurrence of one event has no effect
on the occurrence of the other.
• If A and B are independent events, then
P(A and B)= P(A) • P(B).
Example
• A quality inspector at a bolt manufacturer
randomly selects one both from each
batch of 50 bolts to inspect for problems or
non-conformance. The first batch of 50
bolts has 4 non-conforming bolts. The
second batch of 50 bolts has 5 nonconforming bolts. Find the probability that
the inspector selects a non-conforming
bolt both times.
Solution
• The events are independent. The selection
from the first batch does not affect the
selection from the second batch of bolts.
• P(non-conforming in batch 1) = 4
50
• P(non-conforming in batch 2) =
5
50
• P(non-conforming in both batches) =
4 5
20
1



50 50 2500 125
What are dependent events?
• Dependent events are two events where
the occurrence of one event affects the
occurrence of the other event.
• If A and B are dependent events, then
P(A and B)= P(A) • P(B given A).
Example
• An aquarium contains 6 male goldfish and
4 female goldfish. You randomly select a
fish from the tank, do not replace it, and
then randomly select a second fish. What
is the probability that both fish are male?
Solution
• Because you do not replace the first fish,
the events are dependent.
• P(1st fish male) = 6
10
• P(2nd fish male) =
5
9
• P(male and then male) =
P(male) • P(male given male) =
6 5 30 1
 

10 9 90 3
You try…
1. You choose a card from a standard deck of 52
playing cards. Find the probability that you
choose (a) a heart or a spade, and (b) a card with
an even number or a heart.
2. A basket of apples contains 6 red apples, 2 green
apples, and 3 yellow apples. You randomly select
2 apples, one at a time. Find the probability that
both are yellow if (a) you replace the first apple,
then select the second or (b) you eat the first
apple, then select the second.
Homework:
• Page 354 (all)
• Due Thursday