If you flip two fair coins, what is the probability of getting at most one tail?
Explanation
This question requires identifying the favorable outcomes within a sample space and calculating a simple probability, a core skill from Section 3.1.
Other questions
In probability theory, what is the term for the set of all possible outcomes of a particular experiment?
What does it mean for an event A to have a probability P(A) = 1?
In the context of probability, what does the term 'A OR B' represent?
If two events, A and B, are mutually exclusive, what is the probability of A AND B occurring?
What condition must be met for two events, A and B, to be considered independent?
A student goes to the library. Let B be the event that the student checks out a book, and D be the event that the student checks out a DVD. If P(B) = 0.40, P(D) = 0.30, and P(D|B) = 0.5, what is P(B AND D)?
Using the data from the hiking preference study in Table 3.6, what is the probability that a randomly selected person is a woman OR prefers hiking on mountain peaks?
The law of large numbers, as described in Section 3.1, states that as the number of repetitions of an experiment is increased, the observed relative frequency...
In a standard deck of 52 cards, what is the probability of drawing a red card?
In Example 3.22, Muddy Mouse has three doors to choose from, each with a probability of 1/3. The probability of being caught is 1/5 for Door 1, 1/4 for Door 2, and 1/2 for Door 3. What is the total probability that Alissa the cat does NOT catch Muddy?
What is the primary purpose of a Venn diagram in probability?
In the study on smokers in California and Hawaii (Bringing It Together: Practice, question 59), what is the correct way to find the probability that a randomly selected person was Latino?
What is the formula for the conditional probability of A given B, P(A|B)?
In a bag with six red marbles and four green marbles, you draw two marbles WITH replacement. What is the probability that the first is red and the second is green?
In a bag with six red marbles and four green marbles, you draw two marbles WITHOUT replacement. What is the probability that both are red?
A community swim team has 150 members: 75 advanced, 47 intermediate, and the rest novice. What is the probability that a randomly chosen member is a novice swimmer?
From Example 3.16, 80 of the 150 swim team members practice four times a week. Are being a 'novice swimmer' and 'practicing four times a week' independent events?
What is the complement of event A, denoted A'?
If P(A) = 0.4, what is the probability of its complement, P(A')?
In a survey of 100 individuals organized by gender and coffee/tea preference (Table 3.2), 16 women preferred tea and 36 women preferred coffee. What is P(C|W), the probability that a person prefers coffee given they are a woman?
A six-sided die is rolled. Event A is 'the face is odd' {1, 3, 5} and event C is 'odd faces larger than two' {3, 5}. What is P(C|A)?
Klaus can afford one vacation, choosing between New Zealand (A) and Alaska (B). P(A) = 0.6 and P(B) = 0.35. Since he can only afford one, what is the probability he chooses either New Zealand OR Alaska?
A tree diagram is particularly useful for visualizing and solving what type of probability problems?
Using the data from Table 3.15 about musicians, what is the probability that a randomly selected musician is a woman?
Why might a casino use dice with flat faces and filled-in holes, as mentioned in Section 3.1?
You roll one fair six-sided die. Event E is rolling a number that is at least five. What is P(E)?
In the speed violation and cell phone use study (Example 3.20), what is the probability that a driver had no violation in the last year, given that the driver was a cell phone user?
If sampling is done WITHOUT replacement from a population, the events are considered to be what?
In a box with three red cards and five blue cards, a card is drawn. R is the event a red card is drawn, and B is the event a blue card is drawn. What is P(R AND B)?
If P(A) = 0.6 and P(B) = 0.5, and A and B are independent, what is P(A AND B)?
In a jar of 150 jelly beans, there are 22 red, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange. What is the probability of picking an orange jelly bean?
You are rolling a fair, six-sided die. Let E be the event that it lands on an even number, and M be the event that it lands on a multiple of three. What does P(E|M) mean in words?
If two events U and V are mutually exclusive, with P(U) = 0.26 and P(V) = 0.37, what is P(U OR V)?
In a standard deck of 52 cards, what is the probability of drawing a club?
If S = {1, 2, 3, 4, 5, 6} and A = {1, 2, 3, 4}, what is A', the complement of A?
A box of cookies contains three chocolate and seven butter cookies. Miguel randomly selects and eats a cookie, then selects and eats another. What is the probability that both cookies were chocolate?
In the study of musicians (Table 3.15), are the events 'being a woman musician' and 'learning music in school' mutually exclusive?
The probability that a man develops a certain form of cancer is 0.4567. The probability that a man has at least one false positive test for it is 0.51. What tool should be used to represent this situation and calculate joint probabilities?
According to Table 3.20 (Practice Question 115), what is the probability that a randomly selected person is a White male?
A special deck of cards has 4 green, 3 blue, and 3 red cards. An experiment consists of picking a card, noting its color, and then tossing a coin. What is the probability of picking a blue card first, followed by landing a head on the coin toss?
In the scenario from Homework question 99, where 67,800,000 people speak a language other than English at home out of a population of 331,449,281, what is P(E'), the probability that a person speaks another language at home?
If you roll two fair dice, what is the size of the sample space?
A local restaurant knows the probability a customer orders a pizza (Z) is 0.87 and the probability they order a salad given they ordered a pizza, P(S|Z), is 0.55. What is P(S AND Z)?
In a survey of 100 people, 40 are men (M) and 60 are women (W). 50 people like coffee (C). If P(M AND C) = 0.22, are the events 'being a man' and 'liking coffee' independent?
A shelf holds 12 books, 8 fiction and 4 non-fiction. What is the sample space if one book is randomly selected?
What is always the sum of the probabilities of an event and its complement?
According to the U.S. Crime Index Rates table (Table 3.11), what is the probability of a crime being Robbery AND occurring in Year 2?
The simplified addition rule, P(A OR B) = P(A) + P(B), can only be used when events A and B are what?
Based on Table 3.12 relating weight and height, what is the probability that a randomly chosen individual from this group is Overweight AND Tall?