Download AFM 13.4

AFM 13.4
Probabilities of
Compound Events
P(A and B) = P(A) * P(B)
• If 2 events, A and B are independent,
then the probability of both events is
the product of each individual
probability.
Ex. Find the probability of selecting a
face card, replacing it in the deck, and
then selecting an ace.
• P(face card)
• P(ace)
12
52
4
52
• P(face card and ace)
12 4


52 52
3
169
P(A and B) = P(A) * P(B following A)
• If 2 events, A and are B, are
dependent, then the probability of
both events occurring is the product
of each individual probability.
Ex. Find the probability of selecting a
face card, not replacing it in the deck,
and then selecting an ace.
• P(face card)
• P(ace)
12
52
4
51
• P(face card then ace)
12 4
 
52 51
4
221
Independent or Dependent ?
• The probability of rolling a sum of 7 on the
first toss of two number cubes and a sum of
4 on the second toss.
(independent)
• The probability of randomly selecting two
navy socks from a drawer that contains 6
black and 4 navy socks.
(dependent)
Dependent or Independent
• 1. The probability of selecting a blue marble, not
replacing it, then a yellow marble from a box of 5
blue marbles and 4 yellow marble.
(dependent)
• 2. P(randomly selecting 2 oranges from a bowl of 5
oranges and 4 tangerines, if the first selection is
replaced)
(Independent)
• 3. P( randomly taking 2 blue notebooks from a shelf
which has 4 blue and 3 green notebooks)
(dependent)
Dep or Indep ?
• 4. the probability of removing 13 cards from
a standard deck of cards and all of them be
red.
(dependent)
5. In a bingo game, balls numbered 1 to 75 are
placed in a bin. Balls are randomly drawn
and not replaced. Find the probability for
the first 5 balls drawn.
P( selecting 5 even numbers)
 0.0253
(dependent)
26 25 24 23 22 21 20 19 18 17 16 15 14
           

52 51 50 49 48 47 46 45 44 43 42 41 40
37 36 35 34 33
    
75 74 73 72 71
19
 0.000016
1,160, 054
P(A or B) = P(A) + P(B)
If 2 events, A and are B, are mutually
exclusive, then the probability of either A or B
occurs is the sum of each individual
probability.
• Ex. Bob is a contestant in a game where if he
selects a blue ball or a red ball he gets an allexpenses paid cruise. Bob must select the ball
at random from a box containing 2 blue, 3 red,
9 yellow, and 10 green balls. What is the
probability that he will win the cruise?
Since Bob cannot select a blue and a
red ball at the same time, the events
are mutually exclusive
• P(blue or red)= P(blue) + P(red)
2

24
3

24
5
24
P(A or B) = P(A) + P(B) – P(A and B)
• If 2 events, A and are B, are inclusive, then the
probability of either A or B occurs is the sum of
their probabilities decreased by the probability of
both occurring.
• Ex. Bob has read that the probability for a driver’s
license applicant to pass the road test the first
time is . He also read that the probability of
passing the written examination on the first
attempt is . The probability of passing both on
the first attempt is .
5
6
9
10
4
5
Since it is possible to pass both the
road and written examination, these
events are mutually inclusive.
• P(road exam) + P(written exam) – P(both)
5
6

9
10

4
5

14
15
Mutually exclusive or inclusive ?
• 1. P( tossing 2 number cubes and either one
shows a 4)
inclusive
• 2 P( 2 number cubes being tossed and
showing a sum of 6 or a sum of 9)
Exclusive
• 3. P( selecting an ace or a red card from a
deck of cards)
inclusive
Using combination
• 4. P( randomly picking 5 puppies of which at
least 3 are male puppies, from a group of 5
c(4, 2) c(5, 4)c(4,1) c(5,5)c(4, 0)
male and 4 femalec(5,3)
puppies.



c(9,5)
c(9,5)
c(9,5)
9
exclusive
1


14
60
126

20
126
126
5. From a collection of 6 rock and 5 rap CDs, the
probability that at least 2 are rock from 3
c(6, 2)c(5,1) c(6,3)c(5, 0)


randomly selected.
c(11,3)
c(11,3)
19
75
20
inclusive


165
165
33
Find the probabilities
• P(A and B) = P(A) * P(B)
• P(A and B) = P(A) * P(B following A)
• P(A or B) = P(A) + P(B)
• P(A or B) = P(A) + P(B) – P(A and B)