September 25, 2012
September 25, 2012
Let A = People in the study with pierced ears
Let B = People in the study who are male
September 25, 2012
Conditional probability
The probability that one event happens under the condition that another
event is already known to have happened is called a conditional probability.
Suppose we know that event A has happened. Then the probability that
event B happens given that event A has happened is denoted by P(B|A).
September 25, 2012
Independent Events - Two events A and B are independent if the occurrence
of one event has no effect on the chance that the other event will occur. In
other words, events A and B are independent if
P(A|B) = P(A) and P(B|A) = P(B)
If two events are not independent, we sometimes say that they are
dependent.
Example: Coin Flip
If I toss a coin twice, let Event A = 1st toss is a Head and Event B = 2nd toss is a Head.
Cautionary Note: P(B|A) is not asking what the
probability of tossing two heads will be. It's asking
what the probability that the second toss will result in
getting a Head given that the first toss was a Head. Big
difference!
The coin has no memory, so the whatever happened on
the first toss has absolutely ZERO effect on what will
happen on the next toss. Therefore, P(A|B) = P(A) and P
(B|A) = P(B) in this case!
September 25, 2012
Independent Events verses Mutually Exclusive Events
Example: Rolling Two Dice (one Red, one Green)
Let A = Rolling a 4 on the Red die
Let B = Rolling a sum of 11
What's P(A and B)?
What's P(B|A)?
Is this the same as P(B)?
September 25, 2012
Example (from the book):
7.53 Sampling senators, III
The two-way table at right describes the members of
the U.S. Senate in 2008. Suppose we select a senator at
random. Consider events D = is a Democrat and F = is
female.
(a) Find P(D|F). Explain what this value means.
(b) Find P(F|D). Explain what this value means.
(c) Are events D and F mutually exclusive? Justify your answer.
(d) Are events D and F independent? Justify your answer.