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Jan 206:23 PM
4.2 Probability of compound events
Students will be able to compute the probabilities of compound events.
Test on chapter 3 and 4 on Tuesday 1/25/11
Jan 268:14 AM
Flip a coin, Roll a dieSample Space
P(H, 5) =
P(T, even) =
Students will be able to compute the probabilities of compound events.
2
Jan 268:29 AM
The "And" StatementIndependent Event
the occurrence of one event does not affect the probability of the other
P(A and B) = P(A) . P(B)
P(H and 5) = P(H) . P(5) =
P(T and even) = P(T) . P(even) =
Flip a coin and then roll a die:
Students will be able to compute the probabilities of compound events.
Jan 268:43 AM
Roll A six sided Die, Draw A Card
P(4, King) = P(4 and King) =
P(even, ♦) = P(even and ♦)
Students will be able to compute the probabilities of compound events.
3
Jan 268:48 AM
P(Ace and King) =
Draw a card. Put it back, and draw another card.
Students will be able to compute the probabilities of compound events.
Jan 268:53 AM
Dependent EventsP(A and B) = P(A) . P(B, given that A)P(A and B) = P(B) . P(A, given that B)Extra information. Just remember to change the sample space before doing the second fraction.
P(Ace and Ace) = P(Ace) . P(Ace, given that Ace)
P(Ace) . P(King, given that Ace)
Draw a card. Do not replace it, and draw another card.
P(Ace and King) can be written as
Students will be able to compute the probabilities of compound events.
4
Jan 268:59 AM
The "or" Statement
P(Ace or King) = Count how many
P(Ace) + P(King) =
Mutually ExclusiveEvents that have no outcomes in commonIf there are no common outcomes then P(A or B) = P(A) + P(B)Draw one card from the deck
P(Face card or a 3) = P(face) + P(3)
P(♥ or ♣) =
Jan 269:14 AM
P(Red or face) =P(Red) + P(face) P(Red and face) =
P(Queen or ♥) = P(Queen) + P(♥) P(Queen and ♥) =
Overlapping events!!! Be carefull. Must subtract off the overlapping amount.
Students will be able to compute the probabilities of compound events.
5
Jan 2610:00 AM
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second
P(3 on 1st card and 10 on 2nd) =
Students will be able to compute the probabilities of compound events.
Jan 269:26 AM
At Hopewell Electronics, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers.Employee Political Affiliation RowType Dem.(D) Rep.(R) Ind.(I) TotalsExecutive(E) 5 34 9 48Prod. Workers 63 21 8 92
totals 68 55 17 140
P(D) =
P(E) =
P(D, given that E) =
Students will be able to compute the probabilities of compound events.
answer= 68 = .486 = 49% 140
answer= 48 = .343 = 34% 140
answer= 5 = .104 = 10% 48
6
Jan 2610:07 AM
At Litchfield College of Nursing, 85% of incoming freshmen nursing students are female and 15% are male. Recent records indicate that 70% of the entering female students will graduate with a BSN degree, while 90% of the male students will obtain a BSN degree. If an incoming freshmen nursing student is selected at random, find
P(Student will graduate, given that student is female) =
P(Student is female AND student will graduate) =
Why is P(Student is female AND student will graduate) different from P(Student will graduate, given that student is female)?
Its the Sample Space. In P(Student will graduate, given that student is female) the Sample Space is just the female students. In P(Student is female AND student will graduate) the Sample Space is all students.
Students will be able to compute the probabilities of compound events.
answer: .70 = 70%
These two are different questions!!
answer: (.70)(.85)= .595 = 60%
Jan 159:39 PM
Assignment: p 188 #1,3, 513,15,17,19
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