Vocab
What does a mutually exclusive event mean?
When two outcomes CANNOT occur at the same time
How do you calculate expected value?
Multiply each possible outcome by its probability of occuring, and then add those values together.
A six sided die is rolled two times. What is the probability of rolling a 1 or 2 both times?
0.111
In a card game, players can earn points based on the suit of the card that they randomly draw. Drawing a spade results in +2 points, a club results in +1 point, a diamond results in 0 points, and a heart results in -5 points. What is the expected value of points earned from this game?
0.25(2)+0.25(1)+0.25(0)+0.25(−5) = -0.5
What are the percentages of data that fall 1,2, and 3 standard deviations away from the mean in a normal distribution?
68%, 95%, and 99.7%
How do you find the probability of overlapping events?
P(A or B) = P(A) + P(B) - P (A and B)
There are 50 cookies in a cookie jar. There are 12 chocolate chip cookies, 16 sugar cookies, 9 shortbread cookies, and 13 snickerdoodle cookies. If I close my eyes and randomly pick a cookie from the jar, what is thr probability that the cookie will be a snickerdoodle OR sugar cookie?
29/50, 58%
A student randomly guesses on every question on their 10 question true or false test. What is the probability that atleast 6 questions will be correct?
0.377
TRUE OR FALSE: The sample mean gets further from the true population mean as the sample size increases
FALSE
sample mean gets CLOSER to true pop. mean when sample size increases
P(A and B) = P(A) * P(B given A)
In a classroom, 40% of students have a pet dog, and 30% of students have a pet cat. If 15% have both, what is the probability that a randomly selected student has a cat or a dog?
0.55
A random card is drawn from a deck. Given that the suit is spade, what is the probability it is also a queen or a king?
0.1538 (2/13)
What is the difference between binomial and geometric probability?
BINOMIAL- the number of trials is fixed and it counts the number of succeses
GEOMETRIC- the number of trials until the first success is counted
How do you find the probability of at least one success occuring in k trials?
P(at least one) = 1 - P(no successes)
At a toy shop, 5% of all the toys manufactured are defected. If 20 toys are selected randomly, what is the probability that atleast 3 toys have a defect?
0.075
If you draw 4 cards without replacement from a standard deck of cards, what is the probability that all 4 cards are greater than 7?
0.0392
How do you combine random variables? Explain how to add/subtract means and standard deviations in your answer.
MEANS:
Adding: meanx + meany
Subtracting: mean(x) - mean (y)
VARIANCES:
Add/Sub: Square root of the sum of the squared standard deviations
**cannot add/sub standard dev., must use variances**
What formula would you use to solve:
"In a school with 400 people, 90 people are taking a sculpture class and 130 people are taking a digital imaging class. If the student that is randomly selected takes sculpture, what is the probability that they also take digital imaging?"
Conditional Probability formula
P (taking digital imaging given taking sculpture) = P(dig imaging AND sculpture) divided by P(sculpture)
A bag has 12 red candies, 9 blue candies, and 7 green candies. I will pick 2 candies randomly without replacement. If the first candy I pick is blue, what is the probability that the second candy is green?
0.259 (7/27)
At a school, 55% of students are enrolled in a biology class, 40% of students are enrolled in a calculus class, and 25% are in both. If the random student that is chosen is enrolled in biology, what is the probability they are also enrolled in a calculus class?
0.4545