Any answers are greatly appreciated.
a) In the game of “In-Between” two cards are drawn from a standard deck of 52 cards. Then a third card is drawn. To win, the value of the third card must be between the first two cards. Determine the probability of winning; given the first two cards drawn are a 5 and a 9?
A: 8/25
B. 4/13
C. 3/50
D. 6/25
b) A married couple decides to have a family. They would like to have 5 children and of these 5 children the mother wishes to have exactly 3 girls. If both sexes are equally probable, what is the probability of exactly 3 girls?
A. 5/8
B. ½
C. 5/16
D. 5/32
c) In 7 spins of a spinner the arrow landed on the blue sector at least 3 times. Which of the following is the complement of this event?
A. landing on 0 or 1 or 2 blue sectors
B. landing on 7 blue sectors
C. landing on 1 or 2 or 3 blue sectors
D. landing on more than 3 blue sectors
d) Statistics indicate that 45% of smokers get emphysema while 38% get lung cancer. 12% get both emphysema and lung cancer. What is the probability that a randomly selected smoker does not have either of these diseases?
A. 15%
B. 39%
C. 61%
D. 85%
e) A survey at a high school determines that 69% of teenagers listen to rock music and 33% listen to classical music. 16% listen to neither type of music. What is the probability that a randomly selected student listens to both classical and rock music?
A. 2%
B. 18%
C. 84%
D. 86%
f) A single card is drawn from a standard deck of playing cards. Determine the probability that the card is a diamond or face card.
A. ¼
B. 25/52
C. 3/52
D. 11/26
g) A box contains 7 green marbles and 5 blue marbles. Find the probability of drawing 3 green marbles if the marbles are not replaced after each draw.
A. 77/44
B. 35/288
C. 343/1728
D. 7/12
h) A bag contains 3 white balls and 4 black balls. A second bag has 3 black balls and 6 red balls. If one ball is drawn from each bag, what is the probability that 1 white ball and 1 red ball will be drawn?
A. 2/7
B. 5/21
C. 2/3
D. 23/21
i) In a standard deck of 52 playing cards, 3 cards are selected without replacement. The probability that all 3 cards are 7’s is:
A. 1/5525
B. 1/2197
C. 3/17576
D. 3/125
j) A high school soccer team has 2 goalies, 6 midfielders and 12 forwards. If 3 team members are selected at random what is the probability that all 3 will be forwards?
A. 243/250
B. 1/57
C. 27/125
D. 11/57
k) Team A defeats Team B 60% of the time. During the basketball season Team A and Team B play each other 3 times. What is the probability that Team A will win exactly 2 of the 3 games they play?
A. 0.432
B. 0.360
C. 0.216
D. 0.288
l) The cross-country running team consists of 6 boys and 8 girls. For the next meet the coach must select two co-captains. What is the probability these two co-captains are boys?
A. 3.330x10^-4
B. 48/91
C. 15/91
D. 4/13
m) In a first year University Mathematics class there are 130 females and 110 males. 35 females and 25 males own a cell phone. If a student is randomly selected from the class and that student owns a cell phone, determine the probability the student is a girl.
A. 5/48
B. 19/48
C. 7/48
D. 7/12
n) The student government is holding elections for the school Prime Minister. There are three students running for Prime Minister. Student A is twice as likely to win as student B and student B is twice as likely to win as student C. Determine the probability that student A wins the election.
A. ¾
B. 2/3
C. 4/7
D. 4/5
o) Two cards are dealt without replacement from a well-shuffled deck of 52 cards. Determine the probability the second card is a face card?
A. 11/221
B. 40/221
C. 11/51
D. 3/13
p) A multiple-choice test has 14 questions. Each question has 4 choices and only one of which is correct. If a student answers each question by guessing randomly, the probability that the student gets at least 9 questions correct.
A. 0.0018
B. 0.00034
C. 0.0022
D. 0.9982
q) A diagnostic test was developed to detect a disease. The test is 98% accurate, which means the outcome of the results will be correct 98% of the time. It is known that 10% of the population has the disease. Determine the probability that a randomly selected person tests negative.
A. 0.116
B. 0.020
C. 0.980
D. 0.884
Harrumph. You are asking us to take a 17 question test for you. You have shown no effort at all. That is not what we do here.
In (o) NOT KNOWING what the first card drawn is, the probability of the second card being a face card is 12/52 = 3/13. I could be any card in the original 52 card deck, with equal probability.
Tell us what you think the other answers are and someone will comment on your logic.