Chapter 6 Review Fr Chris Thiel 13 Dec

Chapter 6 Review Fr Chris Thiel 13 Dec 2004

What is true about probability? • The probability of any event must be a number between 0 and 1 inclusive • The sum of all the probabilities of all outcomes in the sample space must be 1 • The probability of an event is the sum of the outcomes in the sample space which make up the event

Independent Previous outcomes do not change probability Multiplication Rule: P(A and B)=P(A)P(B)

Disjoint One outcome precludes the other since there is No overlap…

Complement The event A does not occur

Addition Rules P(A or B)=P(A)+P(B)-P(A and B)

Multiplication Rules P(A and B)=P(A)P(B) if A and B are independent

Conditional Rules

P(65+)=18% P(Widowed)=10% a. If among 65+, 44% widowed, What percent of the population are widows over 65? b. If 8% are widows over 65, What is the chance of being a widow given that they’re over 65? See Table 6. 1 p. 366

Use Venn Diagrams & Trees Venn Diagrams can help see if events are Independent, complementary or disjoint Use Tree Diagrams to Organize addition and Multiplication rules to combinations of events

If event A and B are disjoint, then • P(A and B)= 0 • P(A or B) =1 • P(B)=1 -P(A)

Independent events… you flip a coin and it’s heads 4 times in a row…. The odds are STILL the same

The 6 is 3 times more likely to occur… what is the probability of rolling a 1 or a 6?

A fair die is tossed 4 or 5 -win $1 6 -win $4 If you play twice: what is the probability that you will win $8? $2?

P(A)=. 5 P(B)=. 6 P(A and. B)=. 1 • • • P(A|B)=? Are A and B Independent? Disjoint? Will either A or B always occur? Are A and B complementary?

Lie Detector • Reports “Lie” 10% if person is telling the truth • Reports “Lie” 95% if the person is actually lying • Probability of machine never reporting a lie if 5 truth tellers use it

You enter a lottery, the odds of getting a prize is. 11 If you try 5 times, what is the probability that you will win at least once? • 1 -P(never winning)

8% have a disease. A test detects the disease 96% And falsely indicates the disease 7%. If you test positive, what is the chance you have the disease? P(D|+)

P(Harvard)=40% P(Florida)=50% P(both)=20% P(none)=? P(F but not H)=?

30% of calls result in a airline reservation. a. P(10 calls w/o a reservation)=? b. P(at least 1 out of 10 calls has a reservation)=?

85% fire calls are for medical emergencies Assuming independence… P(exactly one of two calls is for a medical emergency)=? P(M)P(F)+P(F)P(M)=(. 85)(. 15)+(. 15)(. 85)=. 255 Is it really independent?