Conditional Prob.Recall the setting with the pierced ears. 1. If we know that a randomly

selected student has pierced ears,what is the probability that the student is male? P(is male given has pierced ears) =

2. If we know that a randomly selected student is male, what is the probability that the student has pierced ears? P(has pierced ears given is male) =

Pierced EarsGender Yes No TOTAL

Male 19 71 90

Female 84 4 88

TOTAL 103 75 178

Conditional Prob.Conditional Probability – the probability that one event happens given that another event already happened.

We are trying to find the probability that an event will happen under the condition that some other event already happened

If event A already happened, the probability that event B happens given event A has happened is P(B given A) = P(B|A) P(A given B) = P(A|B)

Conditional Prob.If event A = male and event B = pierced ears

P(B|A) =

P(A|B) =

Pg. 314

Pierced EarsGender Yes No TOTAL

Male 19 71 90

Female 84 4 88

TOTAL 103 75 178

IndependenceThe pierced ears problem describes events that were dependent, we used different numbers “depending” on the conditions of the selected students.

When dealing with settings of chance behavior, like tossing a coin, one toss does not effect the other (memory).

Two events A: first toss heads, B: second toss heads. What is the conditional probability that the second toss is a head given that the first toss is a head?

IndependenceWith chance behavior, mutually exclusive events, P(B|A) = P(B) Knowing that the first toss was heads does not affect the probability of the second toss being heads.

Independent events – the knowledge or occurrence of one event does not change or effect the chance or likelihood that another event will happen.

IndependenceAre the events “male” and “left-handedness” independent?*Check to see if two events are independent: does P(B|A) = P(B) ????

Check the P(left-handedness | male) = Check the P(left-handedness) = Are they equal????

HandednessGender Right Left TOTAL

Male 20 3 23

Female 23 4 27

TOTAL 43 7 50

Independence***The two probabilities were

We could have also compared P(male | left-handed) & P(male)

HandednessGender Right Left TOTAL

Male 20 3 23

Female 23 4 27

TOTAL 43 7 50

IndependenceWe found that these events were not independent.

Does that mean there is actually a relationship between gender and handedness???

It is unlikely that these two events are directly related. **These two probabilities should be close to equal if there is no association between the variables.Pg. 317

HandednessGender Right Left TOTAL

Male 20 3 23

Female 23 4 27

TOTAL 43 7 50