Question
In: Statistics and Probability
2.In a high school, 16% are Freshmen, 14% are Sophomores, 38% are Juniors, and 32% are...
2.In a high school, 16% are Freshmen, 14% are Sophomores, 38% are Juniors, and 32% are Seniors. Suppose 15 students are randomly selected. Find the probability that
a) 4 are Freshmen, 5 are Sophomores, and the rest are neither Freshmen nor Sophomores (in any order)
b) either exactly one is Senior and all the others are not Senior (in any order) or exactly one Freshman, one Sophomore, one Junior and all the others are Seniors ( in any order)
Note: For each part, just give the formula as an answer; numerical answer is not required.
3. If seven fair dice are rolled, what is the probability that the number 2 and the number 6 will appear the same number of times?
(Note: “Same number of times” includes both 2 and 6 not appearing at all)
Solutions
orchestra answered 2 years agoRelated Solutions
A nationwide award for high school students is given to outstanding students who are sophomores, juniors,...
A nationwide award for high school students is given to
outstanding students who are sophomores, juniors, or seniors
(freshmen are not eligible). Of the award-winners, 65 percent are
SENIORS, 20 percent JUNIORS, and 15 percent are SOPHOMORES.
Note: Your answers should be expressed as decimals rounded to
three decimal places.
(a) Suppose we select award-winners one at a time and continue
selecting until a SENIOR is selected. What is the probability that
we will select exactly three award-winners?
(b) Suppose...
A nationwide award for high school students is given to outstanding students who are sophomores, juniors,...
A nationwide award for
high school students is given to outstanding students who are
sophomores, juniors, or seniors (freshmen are not eligible). Of the
award-winners, 60 percent are SENIORS, 24 percent JUNIORS, and 16
percent are SOPHOMORES.
Note: Your answers should be expressed as decimals rounded to
three decimal places.
(a) Suppose we select award-winners one at a time and continue
selecting until a SENIOR is selected. What is the probability that
we will select exactly three award-winners?
(b) Suppose...
A study group is to be selected from 5 freshmen, 7 sophomores, and 4 juniors. a....
A study group is to be selected from 5 freshmen, 7 sophomores,
and 4 juniors. a. If a study group is to consist of 4 freshmen, 6
sophomores, and 2 juniors, how many different ways can the study
group be selected? b. If a study group consisting of 6 students is
selected, what is the probability that the group will consist of 2
freshmen, 3 sophomores, and 1 junior?
Six names will be drawn from a group of H+2 freshmen, F+L sophomores, 2*(H-1) juniors, and...
Six names will be drawn from a group of H+2 freshmen, F+L
sophomores, 2*(H-1) juniors, and 2*H seniors. Calculate (rounding
your answers to three decimal places) the probability that:
a. freshmen, sophomores and juniors are equally represented.
Ans.___________
the number of freshmen drawn equates the number of sophomores
and juniors drawn.Ans.___________
the ratio of drawn seniors to drawn sophomores is 3:1.
Ans.___________
the ratio of drawn juniors to drawn freshmen is at least 3:1.
Ans.___________
H= 6
T= 21
F=6...
Six names will be drawn from a group of H+2 freshmen, F+L sophomores, 2*(H-1) juniors, and...
Six names will be drawn from a group of H+2 freshmen, F+L
sophomores, 2*(H-1) juniors, and 2*H seniors. Calculate (rounding
your answers to three decimal places) the probability that:
a. freshmen, sophomores and juniors are equally represented.
Ans.___________
b. the number of freshmen drawn equates the number of sophomores
and juniors drawn. Ans.___________
c. the ratio of drawn seniors to drawn sophomores is 3:1.
Ans.___________
d. the ratio of drawn juniors to drawn freshmen is at least 3:1.
Ans.___
H...
A club has 50 members of which 20 are freshmen, 15 are sophomores, 10 are juniors...
A club has 50 members of which 20 are freshmen, 15 are
sophomores, 10 are juniors and 5 are seniors.
a) How many ways are there to select a president, a
senior vice president, and a vice president if they can not be from
the same class?
b) How many ways are there to select one president, and
two vice presidents if they can not be from the same
class?
Assume that the class consists of 40 percent freshmen, 20 percent sophomores, 20 percent juniors, and...
Assume that the class consists of 40 percent freshmen, 20
percent sophomores, 20 percent juniors, and 20 percent seniors.
Assume further that 40 percent of the freshmen, 45 percent of the
sophomores, 40 percent of the juniors, and 20 percent of the
seniors plan to go to medical school. One student is selected at
random from the class. (1) What is the probability that the student
plans to go to medical school? equation editorEquation Editor (2)
If the student plans...
1. A football team consists of 18 freshmen and 18 sophomores, 15 juniors, and 12 seniors....
1.
A football team consists of 18 freshmen and 18 sophomores, 15
juniors, and 12 seniors.
Four players are selected at random to serve as captains. Find
the probability that at least 1 of the students is a senior.
2.
If a gambler rolls two dice and gets a sum of 10, he wins $10,
and if he gets a sum of
three, he wins $20. The cost to play the game is $5. What is the
expectation of this...
Do freshmen, sophomores, juniors and seniors have the same mean number of hours of homework each...
Do freshmen, sophomores, juniors and seniors have the same mean
number of hours of homework each week? Test at the alpha = .05
level with the following random sample.
Freshmen: { 15, 12, 20, 25}
Sophomores: {20, 12, 14, 15}
Juniors: {25, 10, 10, 15}
Seniors: {15, 12, 12, 14, 9}
Using the given alpha and p-value, what is your conclusion in
plain English?
a) There is not enough evidence to suggest that the population
means are equal.
b)...
Rework problem 25 from section 3.2 of your text, involving choosing freshmen, sophomores, and juniors. For...
Rework problem 25 from section 3.2 of your text, involving
choosing freshmen, sophomores, and juniors. For this problem,
assume that three students are chosen from 3 freshmen, 6
sophomores, and 5 juniors. What is the probability of selecting 2
freshmen and 1 junior given that at least one freshman will be
selected?
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