Question
1 A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or iv) is most likely? (i) H T H
A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or iv) is most likely?
(i)
H T H T H T H T H T H T
(ii)
H T T H H T T H T H H T
(iii)
H H H H H H H H H H H H
(iv)
T T T H T H H H H T H H
- (ii) because there are an equal number of heads and tails but in a random order
- (i) because there are an equal number of heads and tails.
- (iv) because you won't necessarily get the same number of heads and tails with a fair coin
- They are all equally likely.
- (iii) because heads are just as likely as tails
In 2012, researchers working with a very large population of health records found that 9.3% of all Americans had diabetes (source: National Diabetes Statistics Report, 2014). Suppose a medical researcher randomly selects two individuals from a large population.
Let A represent the event "the first individual has diabetes."
Let B represent the event "the second individual has diabetes."
True or false? A and B are independent events.
- True
- False
For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.89 independently of the others.
The bank, obviously, is interested in the probability that when a theft occurs,at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least oneof the 3 systems will detect it?
Your answer should be rounded to 5 decimal places.
Question 4In a certain liberal arts college with about 10,000 students, 57% are males. If two students from this college are selected at random, what is the probability that they are of the same gender?
Your answer should be rounded to 4 decimal places.
Question 5According to the information that comes with a certain prescription drug, when taking this drug, there is a 17% chance of experiencing nausea (N) and a 45% chance of experiencing decreased sexual drive (D). The information also states that there is a 10% chance of experiencing both side effects.
What is the probability of experiencing only nausea?
Your answer should be rounded to two decimal places.
Question 6According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects.
What is the probability of experiencing neither of the side effects?
Your answer should be to two decimal places.
Question 7According to the information that comes with a certain prescription drug, when taking this drug, there is a 24% chance of experiencing nausea (N) and a 42% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects.
What is the probability of experiencing nausea or a decrease in sexual drive?
Your answer should be rounded to 2 decimal places.
Question 8An engineering school reports that 51% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 32% are both male and between the ages of 18 and 20.
What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20?
Your answer should be to two decimal places.
Question 9An engineering school reports that 58% of its students were male (M), 37% of its students were between the ages of 18 and 20 (A), and that 23% were both male and between the ages of 18 and 20.
What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M).
Your answer should be given to two decimal places.
Question 10An engineering school reports that 53% of its students were male (M), 30% of its students were between the ages of 18 and 20 (A), and that 23% were both male and between the ages of 18 and 20.
What is the probability of a random student being male or between the ages of 18 and 20?
Your answer should be rounded to two decimal places.
Question 11Let A and B be two independent events such that P(A) = 0.47 and P(B) = 0.43.
What is P(A or B)?
Your answer should be given to 4 decimal places.
Question 12Let A and B be two independent events such that P(A) = 0.2 and P(B) = 0.7.
What is P(A and B)?
Your answer should be given to 2 decimal places.
Question 13Let A and B be two disjoint events such that P(A) = 0.52 and P(B) = 0.2.
What is P(A and B)?
Question 14Let A and B be two disjoint events such that P(A) = 0.28 and P(B) = 0.52.
What is P(A or B)?
Question 15The following probabilities are based on data collected from U.S. adults. Individuals are placed into a weight category based on weight, height, gender and age.
Underweight
Healthy Weight
Overweight (not Obese)
Obese
Probability
0.021
0.371
0.347
0.261
Based on this data, what is the probability that a randomly selected U.S. adult weighs less than the overweight(but not obese) range?
Your answer should be given to 3 decimal places.
Question 16The probabilities for the amount that can be won on a lottery game are given in the table below. Find the missing probability X.
Amount($)
0
1
2
3
>3
Probability
0.53
0.27
X
0.04
0.01
X =
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started