Transcript Independent and Dependent Events

Independent and Dependent
Events
Slide 1
Independent Events
Whatever happens in one event has absolutely nothing
to do with what will happen next because:
1. The two events are unrelated
OR
2. You repeat an event with an item whose
numbers will not change (eg.: spinners or
dice)
OR
3. You repeat the same activity, but you
REPLACE the item that was removed.
The probability of two independent events, A and B, is equal
to the probability of event A times the probability of event B.
P(A, B) = P(A)  P(B)
Slide 2
Independent Events
Example: Suppose you spin each of these two spinners. What
is the probability of spinning an even number and a vowel?
P(even) =
P(vowel) =
P(even, vowel) =
1
6
P
S
5
2
O
T
3
4
R
Slide 3
Dependent Event
• What happens the during the second event
depends upon what happened before.
• In other words, the result of the second
event will change because of what
happened first.
The probability of two dependent events, A and B, is equal to the
probability of event A times the probability of event B. However,
the probability of event B now depends on event A.
P(A, B) = P(A)  P(B)
Slide 4
Dependent Event
Example: There are 6 black pens and 8 blue pens in a jar. If you
take a pen without looking and then take another pen without
replacing the first, what is the probability that you will get 2
black pens?
P(black first) =
P(black second) =
THEREFORE………………………………………………
P(black, black) =
Slide 5
TEST YOURSELF
Are these dependent or independent events?
1.
Tossing two dice and getting a 6 on both of them.
2.
You have a bag of marbles: 3 blue, 5 white, and 12 red.
You choose one marble out of the bag, look at it then put it
back. Then you choose another marble.
3.
You have a basket of socks. You need to find the
probability of pulling out a black sock and its matching
black sock without putting the first sock back.
4.
You pick the letter Q from a bag containing all the letters of
the alphabet. You do not put the Q back in the bag before
you pick another tile.
Slide 6
Independent Events
Find the probability
• P(jack, factor of 12)
x
=
Slide 7
Independent Events
Find the probability
• P(6, not 5)
x
=
Slide 8
Dependent Events
Find the probability
• P(Q, Q)
• All the letters of the
alphabet are in the
bag 1 time
• Do not replace the
letter
x
=
Slide 9