November 15, 2012
Evaluate the conditional probability of A given B and B
given A using the properties of probablity
Probability - often described as the risk or chance
of something happening
- the ratio that measures the chances of an event
occurring
- a desired outcome is called a success, while any
other outcome is called a failure
- probability of an event occurring is between 0
and 1, the closer to 1, the more likely the event will
occur and the closer to zero, the less likely it will
occur
November 15, 2012
For example:
If I were rolling a die and I needed a 3, the
probability of me rolling a 3 is 1/6
There is one 3 on the die, but a total of 6 possible
numbers.
What is the probability of rolling a number that is
not a 3?
5/6
November 15, 2012
November 15, 2012
November 15, 2012
November 15, 2012
1. Find the probability of drawing a black card.
2. Find the probability of drawing a club.
3. Find the probability of drawing a red ace.
4. Find the probability of drawing a white queen.
5. Find the probability of drawing a card (not including face
cards) higher than 5.
November 15, 2012
Example:
One bag of candy contains 15 red candies, 10
yellow candies, and 6 green candies. Find the
probability of each selection.
a) P(picking a red candy)
15/31
b) P(picking a green candy)
6/31
c) P(not picking a yellow candy)
21/31
d) P(not picking a red or green candy) 10/31
e) P(orange)
0/31
November 15, 2012
The probability that event B will occur given that
another event, A, has already occurred is called a
conditional probability.
P(B | A) = the probability of event B, given event A
P(A | B) = the probability of event A, given event B
P(B | A) = P(A and B)
P(A)
November 15, 2012
Example:
A card is drawn from a standard deck of cards. Find the P
(club) given that the card drawn is black.
P(B | A) = P(A and B)
P(A)
P(club | black) = P(black club)
P(black)
P(club | black) = 2 = 1
26
13
November 15, 2012
On Your own:
A card is drawn from a standard deck of cards. Find the P(4)
given that the card drawn is black.