Probability Rules
How are basic probabilities different from conditional probabilities?
Conditional probability focuses on the total for the condition, while basic probabilities focus on the entire total
If a single fair die is rolled, find P(3 | prime).
1/4
How can you determine if a game is fair?
If the expected value = 0
Are these complementary events
It will rain tomorrow, it will be sunny tomorrow.
No
The rule for finding the probability of rolling a fair die three times and getting three fours.
P(4)3--> (1/6)3
What is the relationship between A and Ac
Ac is the opposite of event A occurring. These probabilities should combine to equal 1
If two cards are drawn without replacement from a deck, find the probability that the second card is a diamond, given that the first card was a diamond.
.235
500 Tickets are sold at $5 apiece for a raffle. There is a grand prize of ______, two second prizes of $250, and five third prizes of $100. if the expected value is -$2.00 What is the amount of the grand prize of the game?
$500 grand prize
John plays the lottery every week. Every time he plays he has a 25% chance of winning a prize. Determine the probability he will win at least one prize if he plays for 10 weeks.
If A and B are independent events, P(A) = 0.35, and P(B) = 0.55, find P(A|B)
.35
True or false
If the success rate of a space mission is 85%, then the probability of having thirty successful missions in a row is .85 x 30
False
A computer technician notes that 40% of computers fail because of the hard drive, 25% because of the monitor, 20% because of a disk drive, and 15% because of the microprocessor. If the problem is not in the monitor, what is the probability that it is in the hard drive?
.533
You pay $1 to play a game in which a pair of fair dice are rolled.If a six, seven, or eight comes up, you win $5; if a two or 12 comes up, you win $3; otherwise, you lose the dollar you paid to play the game. What is the expected value of the game?
Gain $1.39
Suppose A and B are two events of a sample space S where P(A) = 0.28, P(B) = 0.24,
What is P(Ac ∩ Bc).
.547
Suppose A and B are two events of a sample space S where P(A) = 0.28, P(B) = 0.24, and P(A ∪ B) = 0.42. Are these events independent or dependent?
Dependent
How can we determine if two events are independent?
The Pew Internet and American Life Project finds that 93% of teenagers (ages 12 to 19) have a cell phone, and that 75% of teens with phones have an instagram profile, while 11% of teens without a phone has an instagram profile. Given that a person has an instagram profile, what is the probability the person does not have a phone?
1.1%
a card is drawn from a standard 52-card deck. You pay $5 to play the game, which must be subtracted from your winnings. Which of the games below is most beneficial to play
A) If a heart is drawn, you win $10; otherwise, you lose your $5.
B)If an Ace is drawn, you win $30; otherwise, you lose your $5.
Game A
A racing driver needs at least two points altogether in the next five races to win the championship. Each race he has a 30% chance of finishing in the top 5. What is the probability that he finishes outside of the top 5 at least once.
99.7%
In a survey of 1000 eligible voters selected at random, it was found that 200 had a college degree. Additionally, it was found that 70% of those who had a college degree voted in the last presidential election, whereas 45% of the people who did not have a college degree voted in the last presidential election. Given that a person did not vote, what is the probability they did not earn a college degree?
88%
Explain the error in the statements below.
The probability that you choose a woman is 0.52. The probability that the person you choose has never married is 0.25. The probability that you choose a woman who has never married is 0.11.
The probability that the person you choose is either a woman or has never been married (or both) is therefore about .77.
They double counted the women who have never been married.
Five hundred people used a home test for HIV, and then all underwent more conclusive hospital testing. 60 of the 500 tested positive. Out of the positive test, 35 actually had HIV, while only 5 of the negative tests had HIV.
What is the false–positive rate? That is, what is the probability of testing positive given that the person does not have HIV?
.054
A spinner is used that is 60% red and 40% blue. Player A wins if the spinner lands on red. Player B wins in the spinner lands on blue.How would you assign point values so that this game is fair?
Red should be 4 points, Blue should be 6 points
Dystopia county has three bridges. In the next year, the Elder bridge has an 8% chance of collapse, the Younger bridge has a 3% chance of collapse, and the Ancient bridge has a 19% chance of collapse. What is the probability that exactly one of these bridges will collapse in the next year?
.2548
Suppose we have two pairs of dice (these are called Efron’s dice) numbered as follows.
Pair One: Red: 2, 2, 2, 2, 6, 6 Green: 5, 5, 6, 6, 6, 6
Pair Two: Red: 1, 1, 1, 5, 5, 5 Green: 4, 4, 4, 4, 12, 12
If you were to play a game in which the highest total wins when you roll, what is the better pair to play with?
Pair 2