1. A consumer organization estimates that 30% of the households in a particular community have one television set, 39% have two sets, and 20% have three or more sets. What is the probability that a household chosen at random does not have two sets?
A) 0.39
B) 0.80
C) 0.61
D) 0.20
E) 0.50
2. An Imaginary Poll in April 2005 asked 920 U.S. adults what their main source of news was: newspapers, television, internet, or radio. 681 stated that their main source of news was the internet.
Find the probability that a randomly selected U.S. adult stated that their main source of news was not the internet.
A) 0.74
B) 0.681
C) 0.50
D) 0.26
E) 0.239
3. Five multiple choice questions, each with four possible answers, appear on your history exam. What is the probability that if you just guess, you get at least one question wrong?
A) 0.20
B) 0.99902
C) 0.00098
D) 1.000
E) 0.25
4. Suppose a basketball player is an excellent free throw shooter and makes 99% of his free throws (i.e., he has a 99% chance of making a single free throw). Assume that free throw shots are independent of one another. Find the probability that the player will make three consecutive free throws.
A) 0
B) 1
C) 0.9703
D) 0.0297
5. The instructor in a Humanities class says that students have a 15% probability of making an A in her class, 20% probabilty of making a B, 25% chance of making a C, and 20% chance of making a D. The possible grades that can be assigned are A, B, C, D, and F.
What is the probability of a grade less than a C?
A) 65%
B) 20%
C) 25%
D) Cannot be determined from the information given.
E) 40% (This one?)
F) 1%
1. To find the probability that a household chosen at random does not have two sets, we need to find the complement of the probability that a household chosen at random does have two sets.
So, we can calculate the probability that a household chosen at random does have two sets as 39%.
The probability that a household chosen at random does not have two sets is equal to 1 - 0.39 = 0.61.
Therefore, the answer is C) 0.61.
2. The probability that a randomly selected U.S. adult stated that their main source of news was not the internet can be found by subtracting the probability that their main source of news was the internet from 1.
The number of U.S. adults who stated that their main source of news was the internet is 681 out of 920.
So, the probability that their main source of news was not the internet is (920 - 681) / 920 = 239 / 920 ≈ 0.2598.
Therefore, the answer is D) 0.26.
3. The probability of guessing one question correctly is 1/4, and the probability of guessing one question wrong is 3/4.
To find the probability of getting at least one question wrong if you just guess, we can find the complement of getting all questions right.
The probability of getting all questions right is (1/4) * (1/4) * (1/4) * (1/4) * (1/4) = 1/1024.
So, the probability of getting at least one question wrong is equal to 1 - 1/1024 = 1023/1024 ≈ 0.99902.
Therefore, the answer is B) 0.99902.
4. The probability of making a free throw is 99% or 0.99.
Since the free throw shots are independent of each other, the probability of making three consecutive free throws is (0.99) * (0.99) * (0.99) = 0.9703.
Therefore, the answer is C) 0.9703.
5. To find the probability of a grade less than a C, we need to add up the probabilities of getting grades of D and F.
The probability of making a D is 20%, and the probability of making an F can be calculated by subtracting the probabilities of making A, B, C, and D from 1: 1 - (0.15 + 0.20 + 0.25 + 0.20) = 1 - 0.80 = 0.20.
Therefore, the probability of a grade less than a C is 0.20 + 0.20 = 0.40.
Therefore, the answer is E) 40%.
1. To find the probability that a household does not have two sets, we need to subtract the percentage of households that have two sets from 100%.
Given that 39% of households have two sets, the percentage of households that do not have two sets is:
100% - 39% = 61%
Therefore, the probability that a randomly chosen household does not have two sets is 0.61 (or 61%).
So, the correct answer is C) 0.61.
2. To find the probability that a randomly selected U.S. adult stated that their main source of news was not the internet, we need to subtract the percentage of adults who stated their main source of news was the internet from 100%.
Given that 681 adults stated their main source of news was the internet, the percentage of adults who did not state the internet as their main source of news is:
100% - 681/920 * 100% = 26%
Therefore, the probability that a randomly selected U.S. adult stated that their main source of news was not the internet is 0.26 (or 26%).
So, the correct answer is D) 0.26.
3. To find the probability of getting at least one question wrong when guessing on a multiple choice exam with five questions, we need to find the probability of getting all the questions right and subtract that from 1.
For each question, there are four possible answers, so the probability of guessing the correct answer for any given question is 1/4.
To find the probability of getting all the questions right, we multiply the probabilities together:
(1/4) * (1/4) * (1/4) * (1/4) * (1/4) = 1/1024
So, the probability of getting at least one question wrong is:
1 - 1/1024 = 1023/1024
Therefore, the probability of getting at least one question wrong is approximately 0.99902.
So, the correct answer is B) 0.99902.
4. Since the basketball player has a 99% chance of making a free throw, the probability of making a single free throw is 0.99.
Assuming that free throw shots are independent of one another (which means that the outcome of one shot does not affect the outcome of another), the probability of making three consecutive free throws is:
0.99 * 0.99 * 0.99 = 0.9703
Therefore, the probability that the player will make three consecutive free throws is approximately 0.9703.
So, the correct answer is C) 0.9703.
5. To find the probability of a grade less than a C, we need to add up the probabilities of making a D or an F.
Given that the probabilities of making a C, D, and F are 25%, 20%, and some unknown percentage, respectively, we can subtract the sum of these probabilities from 100% to find the probability of a grade less than a C.
100% - 25% - 20% = 55%
Since we don't know the exact percentage of the F grade, we cannot determine the exact probability. However, we know that it must be less than or equal to 55%.
Therefore, the correct answer is D) Cannot be determined from the information given.