9.7 Independent and Dependent Events
Independent events: The occurrence of one event
does not affect the probability of the other.
Example: You roll a die and try to get a 3 and then you
flip a coin and try to get heads
Example: You roll a die and try to get a 3 and then you
roll the die and try to get a 5.
Dependent events: The occurrence of one does affect
the probability of the other.
Example: Drawing a heart and a spade at the same
time from a deck of cards
Example: Drawing a heart from a deck of cards, not
replacing it, then drawing a spade from the deck
Finding Probability for Independent Events
If A and B are independent events, then
P(A and B) = P(A)
P(B)
You are going to roll a die 4 times.
What is the probability that you will get a 5 all four times?
You spin the spinner 3 times
What is the probability
you will spin an even
number all 3 times?
2
1
7
6
3
5
4
Finding Probability of Dependent Events
If A and B are dependent events, then
P(A and B) = P(A)
P(B after A)
You have a bag with 4 red marbles and 6 blue marbles.
You draw a marble from the bag and then
another without replacing the first marble.
What is the probability you will draw 2 red marbles?
A drawer contains 10 black socks and 6 blue socks.
If 2 socks are drawn at random, what is the probability
of getting a pair of black socks?
If 2 socks are drawn at random, what is the probability
of getting a pair of socks of the same color?
(There's 2 possibilities: a pair of black or a pair of
blue - so we need to find the probability of each...)
P(2 black socks) =
P(2 blue socks) =
P(a matching pair) = P(2 black socks) + P(2 blue socks)