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JMAP Solutions – PROBABILITY: Binomial Probability
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BINOMIAL PROBABILITY
MATH B APPEARANCES:
080334b 6-pointer
080128b, 010229b, 060331b, 010428b, 080430b, 060529b,
080630b, 010731b 4-pointer
060122b, 060223b, 010524b, 080522b, 010625b, 060625b
2-pointer
080201b, 010302b, 060402b multiple choice
REGENTS QUESTIONS
SOLUTIONS
010302b
(1)
1
The probability that Kyla
will score above a 90 on
4
a mathematics test is
.
5
What is the probability
that she will score above
a 90 on three of the four
tests this quarter?
4 1
3 4 1
(1) 4 C3 ( ) 3 ( )1
(3) ( ) 3 ( )1
5 5
4 5 5
4 1 1 3
3 4 1
(2) 4 C3 ( ) ( )
(4) ( )1 ( ) 3
5 5
4 5 5
2
4
(1)
060402b
The Hiking Club plans to
go camping in a State
park
where
the
probability of rain on
any given day is 0.7.
Which expression can be
used
to
find
the
probability that it will
rain on exactly three of the
seven
days
they
are
there?
3
4
(1)
(3)
7 C3 ( 0.7) ( 0.3)
C3 ( 0.7) 3 (0.7) 4
3
4
(2)
7 C3 ( 0.3) ( 0.7)
4 1
C3 ( ) 3 ( )1
5 5
7
C3 ( 0.7) 3 (0.3) 4
4
4
4
3
C3 ( 0.4) ( 0.3)
(4)
3
080201b
Which fraction represents
the
probability
of
obtaining
exactly
eight
(1)
1 8 1 2
45
10 C8 ( ) ( ) =
2 2
1024
JMAP Solutions – PROBABILITY: Binomial Probability
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heads in ten
fair coin?
45
(1)
(3)
1,024
64
(2)
(4)
1,024
4
tosses of a
90
1,024
180
1,024
060122b
At
a
certain
intersection,
the light
for eastbound traffic is
red
for
15
seconds,
yellow for 5 seconds, and
green
for
30
seconds.
Find, to the nearest tenth,
the probability that out
of
the
next
eight
eastbound
cars
that
arrive randomly at the
light, exactly three will
be
stopped
by
a
red
light.
5
The
probability
If the probability that
it will rain on any given
day this week is 60%,
find the probability it
will rain exactly 3 out of 7
days this week.
7
080522b
red
light
is
P(3 stopped) =
8
3
7
25412184
C3 ( ) 3 ( ) 5 =
≈ .3
10 10
100000000
060223b
010524b
a
15
3
=
.
15 + 5 + 30 10
3
After studying a couple’s
family history, a doctor
determines
that
the
probability of any child
born
to
this
couple
having a gene for disease
X is 1 out of 4. If the
couple
has
three
children,
what
is
the
probability that exactly two
of the children have the
gene for disease X?
6
of
7
1 3
9
C 2 ( ) 2 ( )1 =
4 4
64
3 2
15120
C3 ( ) 3 ( ) 4 =
5 5
78125
Since there are two even-numbered
channels, the probability of selecting an
JMAP Solutions – PROBABILITY: Binomial Probability
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The Coolidge family's favorite
2 1
= .
television channels are 3, 6, 7, even number is 6 3
10, 11, and 13. If the Coolidge
family selects a favorite channel
1 3 2 2
40
P(3 evens) = 5 C 3 ( ) ( ) =
at random to view each night,
3 3
243
what is the probability that they
choose exactly three evennumbered channels in five nights?
Express your answer as a fraction
or as a decimal rounded to four
decimal places.
8
010625b
6
During a recent survey, students at
Franconia College were asked if they
drink coffee in the morning. The
results showed that two-thirds of the
students drink coffee in the morning
and the remainder do not. What is the
probability that of six students
selected at random, exactly two of
them drink coffee in the morning?
Express your answer as a fraction or
as a decimal rounded to four decimal
places.
9
060625b
Ginger and Mary Anne are
planning a vacation trip to the
island of Capri, where the
probability of rain on any day is
0.3. What is the probability that
during their five days on the
island, they have no rain on
exactly three of the five days?
1
0 As
080128b
2 1
20
C2 ( ) 2 ( ) 4 =
3 3
243
Note the problem gives you the value of q,
instead of p.
5
7
3
3087
C3 ( ) 3 ( ) 2 =
10 10
10000
The areas of the circles are 81π and 9π.
Therefore the probability of hitting the
shown
in
the
accompanying
diagram, a bull’s-eye is 9π = 1 .
81π
9
circular target with a
radius of 9 inches has a
bull’s-eye
that
has
a
1 4 8 1
40
P(4 hits) = 5 C 4 ( ) ( ) =
radius of 3 inches. If
9 9
59049
five arrows randomly hit
1 5 8 0
1
the target, what is the
P(5 hits) = 5 C 5 ( ) ( ) =
probability that at least
9 9
59049
four hit the bull’s-eye?
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Add these two fractions to calculate the
probability of at least four hits:
1
1 Team
010229b
1
2 On
060331b
1
3 Tim
080430b
1
4 The
060529b
41
59049
1 2
40
3 3
243
1 4 2 1 10
P(4 wins) = 5 C 4 ( ) ( ) =
3 3
243
1 5 2 0
1
P(5 wins) = 5 C 5 ( ) ( ) =
3 3
243
3
2
P(3 wins) = 5 C 3 ( ) ( ) =
A and team B are
playing in a league. They
will play each other five
times. If the probability
that team A wins a game is
1
,
what
is
the
3
Add these three fractions to calculate the
probability that team A
51
will win at least three of probability of at least three wins: 243
the five games?
2 3
1344
5 5
78125
2 7 3 0
128
P(7 dinners) = 7 C 7 ( ) ( ) =
5 5
78125
6
1
P(6 dinners) = 7 C 6 ( ) ( ) =
any given day, the
probability
that
the
entire Watson family eats
2
dinner together is
.
Add these two fractions to calculate the
5
Find
the
probability
1472
that, during any 7-day probability of at least six dinners:
78125
period, the Watsons eat
dinner together at least six
times.
1 4 9 1
45
) ( ) =
10 10
100000
1 5 9 0
1
P(5 homers) = 5 C 5 ( ) ( ) =
10 10
100000
P(4 homers) = 5 C 4 (
Parker,
a
star
baseball player, hits one
home run for every ten
times he is at bat. If
Parker goes to bat five Add these two fractions to calculate the
times
during
tonight’s
game,
what
is
the probability of at least four homers: 46
probability that he will
100000
hit at least four home runs?
probability
that
a
planted
3
4
1
4
5
2
P(5 sprouts) = 7 C 5 ( ) ( ) =
5103
16384
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3
3 6 1 1 5103
. If
P(6 sprouts) = 7 C 6 ( ) ( ) =
4
4 4
16384
Peyton plants seven seeds from a slice
3 7 1 0 2187
P(7 sprouts) = 7 C 7 ( ) ( ) =
of watermelon, find, to the nearest ten
4 4
16384
thousandth, the probability that at
least five will sprout.
Add these three fractions to calculate the
watermelon seed will sprout is
probability
of
at
least
five
sprouts:
12393
≈ .7564
16384
1
080630b
5 On mornings when school is in
1 2
40
3 3
243
1 4 2 1 10
P(4 times late) = 5 C 4 ( ) ( ) =
3 3
243
1 5 2 0
1
P(5 times late) = 5 C 5 ( ) ( ) =
3 3
243
3
2
P(3 times late) = 5 C 3 ( ) ( ) =
session in January, Sara notices
that her school bus is late onethird of the time. What is the
probability that during a 5-day
school week in January her bus
will be late at least three times?
Add these three fractions to calculate the
probability the bus will be late at least three
times:
1
6 A
010428b
board
game
has
a
spinner on a circle that
has five equal sectors,
numbered 1, 2, 3, 4, and
5,
respectively.
If
a
player has four spins,
find the probability that
the player spins an even
number no more than two
times
on
those
four
spins.
51
243
Since there are two even numbers, the
probability of spinning an even number is
2
.
5
2 3
5 5
2 1 3 3
P(1 evens) = 4 C1 ( ) ( ) =
5 5
2 2 3 2
P(2 evens) = 4 C 2 ( ) ( ) =
5 5
0
4
P(0 evens) = 4 C 0 ( ) ( ) =
81
625
216
625
216
625
Add these three fractions to calculate the
probability of no more than two even
numbers:
1
010731b
7 Dr. Glendon, the school physician
513
625
4
1
P(4 students) = 5 C4 (.39) (.61) ≈ .071
5
0
P(5 students) = 5 C5 (.39) (.61) ≈ .009
in charge of giving sports
physicals, has compiled his Add to calculate the probability of at
information and has determined least four students: .08
JMAP Solutions – PROBABILITY: Binomial Probability
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that the probability a student
will be on a team is 0.39.
Yesterday, Dr. Glendon examined
five students chosen at random.
Find, to the nearest hundredth,
the probability that at least four
of the five students will be on a
team.
Find, to the nearest hundredth,
the probability that exactly one
of the five students will not be on
a team.
1
8 When
080334b
1
4
P(1 student) = 5 C1 (.61) (.39) ≈ .07
6 3 4 1 3456
) ( ) =
10 10
10000
6 4 4 0 1296
P(4 strikes) = 4 C 4 ( ) ( ) =
10 10
10000
P(3 strikes) = 4 C 3 (
Joe bowls, he can
get a strike (knock down
all the pins) 60% of the
time. How many times more
likely is it for Joe to
Add these two fractions to calculate the
bowl at least three strikes
out of four tries as it probability of at least three strikes: 4752 .
10000
is for him to bowl zero
strikes
out
of
four
tries? Round your answer
6 0 4 4
256
P(0 strikes) = 4 C 0 ( ) ( ) =
to the nearest whole number.
10 10
10000
4752
10000 = 18.5625 ≈ 19
256
10000