Events Involving AND Conditional Probability 11'7

1
Events Involving AND Conditional Probability
11.7
Independent Events When one outcome does not
affect the probability of the other outcome.
P ( A and B) P ( A ) x P ( B )
Dependent Events When one outcome does affect
the probability of the other outcome.
P ( A and B) P(A) x P( B given A has occurred )
2
The spinner shown has equally probability that
the pointer will land on any of the six regions.
If the spinner lands on the border line, spin
again. If the pointer is spun twice, find the
probability it will land on
green then red.
P ( G and R) P ( G ) x P ( R )
3
The spinner shown has equally probability that
the pointer will land on any of the six regions.
If the spinner lands on the border line, spin
again. If the pointer is spun twice, find the
probability it will land on
a color other than red each time.
P ( N R and N R) P ( NR ) x P (NR )
4
The spinner shown has equally probability that
the pointer will land on any of the six regions.
If the spinner lands on the border line, spin
again. If the pointer is spun three times, find
the probability it will land on
green, then red, and then yellow.
P ( G and R and Y) P(G) x P(R) x P(Y)
5
An ice chest contains six cans of apple juice,
eight cans of grape juice, four cans of orange
juice, and two cans of mango juice. Suppose you
reach into the chest to get three drinks for you
and two other people. Find the probability of
selecting
three cans of grape juice.
P ( A and B) P(A) x P( B given A has occurred )
P (G and G and G)
6
An ice chest contains six cans of apple juice,
eight cans of grape juice, four cans of orange
juice, and two cans of mango juice. Suppose you
reach into the chest to get three drinks for you
and two other people. Find the probability of
selecting
grape, then orange, then, mango juice.
P ( A and B) P(A) x P( B given A has occurred )
P (G and O and M)
7
Find the probability of drawing the card listed
and replacing back in the deck shuffle and draw
the second card listed, assume the cards are
drawn from a standard deck of cards
A king and a king.
P (K and K)
A picture card and then a heart.
P (Pic and H)
8
Conditional Probability The probability that an
event B occurs if the sample space is restricted
to the outcomes associated with event A.
Number of outcomes common to B and A
P (B A)
Number of outcomes in A
P (B A)
9
The numbered disks shown are placed in a box and
one disk is selected at random. Find the
probability of selecting
1
2
3
4
5
6
7
8
a 3,given that a red disk is selected.
P (B A)
P ( 3 Red selected)
10
The numbered disks shown are placed in a box and
one disk is selected at random. Find the
probability of selecting
1
2
3
4
5
6
7
8
an even number, given that a yellow disk is
selected.
P (B A)
P ( even Yellow selected)
11
The numbered disks shown are placed in a box and
one disk is selected at random. Find the
probability of selecting
1
2
3
4
5
6
7
8
a yellow disk, given that an odd number is
selected.
P (B A)
P ( Yellow Odd number)
12
Example
If you toss a fair coin seven times what is the
probability of getting all tails?
Independent Event !!!
P ( T,T,T,T,T,T,T)
13
Example
A group of 5 Democrats, 6 Republicans, and 4
Independents need to form a group of two people
to attend a convention. If the two are randomly
selected, find the probability of selecting an
Independent and then a Republican.
Dependent Event !!!
P ( I and R)
14
Table shows differences in political ideology, by
education, for a random sample of U.S. voters.
15
Find the probability, using the table, that a
randomly selected person from this group
is not liberal.
P ( not Liberal)
16
Find the probability, using the table, that a
randomly selected person from this group
is moderate or liberal.
P ( M or L)
17
Find the probability, using the table, that a
randomly selected person from this group
attended H.S. only, given a conservative
ideology.
P ( HS C)
18
Find the probability, using the table, that two
people randomly selected, in succession, from
this group
a moderate and then a liberal.
P ( M and L)
19
Homework

• Pg 612-613
• 3 69 multi of 3