You have two standard decks of cards. You draw one card from each deck. What is the probability that both cards are Aces?
1/26
1/52
1/169
1/13
What does a conditional probability P(Y=y | X=x) represent in the context of joint distributions?
The probability of Y = y, given no information about X
The probability of X = x and Y = y occurring simultaneously
The probability of X = x, given no information about Y
The probability of Y = y, given that X is known to have the value x
A box contains 4 green marbles and 6 red marbles. Two marbles are drawn one after the other without replacement. What is the probability that the first marble is green and the second is red?
1/6
4/15
6/25
2/15
The weight of apples is normally distributed with a mean of 150g and a standard deviation of 10g. What is the z-score for an apple weighing 165g?
-0.67
-1.5
1.5
0.67
The time until a radioactive particle decays is modeled by an exponential distribution. If the average decay time is 10 seconds, what is the median decay time?
10 seconds
14.43 seconds
6.93 seconds
5 seconds
A bag contains 5 red balls and 3 blue balls. Two balls are drawn randomly without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?
5/7
5/8
3/8
2/7
The time until a computer system crashes is exponentially distributed with a mean of 2500 hours. What is the probability that the system will crash within the first 1000 hours?
0.6703
0.1813
0.5
0.3297
Which of the following is NOT an assumption or condition that should be met when applying the Central Limit Theorem?
The population standard deviation needs to be known or estimated.
The samples should be independent of each other.
The sample size should be sufficiently large (generally n ≥ 30).
The population data must be normally distributed.
Given a joint probability distribution table for two discrete random variables X and Y, what does the sum of all probabilities in the table always equal?
0
The expected value of Y
The expected value of X
1
A bag contains 5 red marbles and 5 blue marbles. You draw two marbles from the bag without replacement. What is the probability that both marbles are red?
1/2
2/9
1/9
1/4