3.1-3.4
This term is denoted by S and consists of all possible sample points/outcomes
What is a sample space?
What is the formula for the multiplicative rule of probability for two independent events?
What is P(A)P(B)?
The number of fish caught during a fishing tournament.
Discrete
(you can't catch .6 fish)
Is the expected value of the probability distribution of a random variable always one of the possible values of x? Explain.
What is no, because the expected value represents the average value of x over a large number of trials?
How many total sample points are there in total if we flip a coin 9 times?
What is 512?
How many possible ways are there to select 2 cards from a full deck without replacement?
What is 2652
(52 x 51)
For two events, A and B, P(A)=0.4, P(B)=0.5, and P(A&B)=0.2.
Are events A and B independent?
Yes.
( P(A|B)=P(A) )
The random variable x has the following discrete probability distribution.
x -5 3 6 7 9
p(x) 0.1 0.2 0.1 0.2 0.4
What is the probability that x is greater than -3?
What is 0.9?
(Add probabilities that belong to x values larger than -3)
Consider the following probability distribution and calculate mean.
x 20 30 40 50 60 70
p(x) .15 .2 .35 .15 .1 .05
What is mean of 44?
20(.15)+30(.2)...
Does this situation result in a binomial distribution? Why?
Drawing 5 cards from a deck, without replacement, and counting the number of clubs.
What is no?
(trials are not independent so probability changes)
Suppose that you guess at a multiple choice question with 5 possible answers and a true/false question.
What is the chance you guess at both questions and get both questions correct?
What is 1/10?
(1/5 x 1/2)
According to a study, one-fifth of all rough diamonds produced in one region are blood diamonds. Also, 39% of the region's rough diamonds are processed in City X, and of these diamonds, one-third are blood diamonds.
What is the probability that a rough diamond produced in this region is not a blood diamond?
What is 4/5?
(complement of P(A), which is 1/5 (probability of all rough diamonds produced in this region are blood diamonds)
Five coins are tossed. Let x equal the number of tails observed.
What are the possible values of x?
What are x= 0, 1, 2, 3, 4, 5
A journal published a study on the number of insect eggs on a blade of water hyacinth. Fine the mean.
x 1 2 3 4
p(x) .39 .46 .03 .12
What is 1.88?
(1x.39)+2(.46)...
A student guesses at 6 multiple choice questions with 4 possible answers each (A, B, C, D). Create a probability distribution for x = the number of questions answered correctly.
x 0 1 2 3 4 5 6
p(x) .1780 .3560 .2966 .1318 .0330 .0044 .0002
Suppose that you make a completely random guess at a multiple choice question with 5 possible answers and a true/false question.
What is the probability that you get the first question correct OR the second question correct?
What is 0.6?
(1/5 + 1/2 - 1/10)
For two events, A and B, P(A) = 0.4, P(B) = 0.4, and P(A|B) = 0.5
Find P(A|B).
What is 0.5?
P(A|B) = P(A&B) / P(A)
Three fair coins are tossed. Let x equal the number of tails observed.
Create a probability distribution.
What is:
x 0 1 2 3
p(x) .125 .375 .375 .125
In a casino game, you can bet whether one ball will fall in an arc on a wheel colored red, black, or green. Say the probability of a red outcome is 18/38, a black outcome is 18/38, and a green outcome is 2/38. Suppose someone makes a $25 bet on black in the hopes of winning a $50 prize. Find the expected net winnings for this bet if it was made a large number of times.
What is an expected value of -1.316?
(fill outcomes and probabilities into L1 and L2 and calculate 2-var stats with L2 for Freq)Elise guesses at 20 multiple choice questions with 4 possible answers each. What is the probability that she answers 3, 4, or 5 of them correctly?
.526
binompdf(20, .25, 13/14/15) and add
An institute mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than 2 should have an incorrect price. A recent study of the accuracy of checkout scanners of the stores of a certain company showed that, of the 75 stores investigated, 60 violated the institute scanner accuracy standard. If 1 of the 75 company stores is randomly selected, what is the probability that that store does not violate the Institute scanner accuracy standard?
What is .20?
The probability that speeding is a cause of a fatal car crash is 0.34. Furthermore, the probability that speeding and missing a curve are causes of a fatal crash is 0.17. Given that speeding is a cause of a fatal crash, what is the probability that the crash occurred on a curve?
What is .5?
P(A|B)= P(A&B) / P(A) -> 0.17 / 0.34 = .5
A weapons manufacturer uses a liquid propellant that can get mixed with another liquid to produce a contaminated cartridge. A statistician found that 24% of the cartridges in the particular lot were contaminated. Suppose you randomly sample (without replacement) gun cartridges from this lot until you find a contaminated one. Let x be the number of cartridges sampled until a contaminated one is found.Use the formula below to find P(x=1).
P(x) = (0.24)(0.76)x-
.240
A basketball player makes 80% of his free throws. The table shows the number of free throws we expect him to make out of his next 6. Find the mean, standard deviation, and any unusual values of x.
x 0 1 2 3 4 5 6
p(x) .001 .005 .014 .08 .25 .39 .26
What is:
mean: 4.783
standard dev: 1.007
unusual: 0, 1, 2
A lottery sells $1 tickets to win a $5,000,000 prize. The odds of winning are about 1 in 22 million. What are the expected net winnings for entering this lottery with a single ticket?
What is -0.77?