A study shows that 60% of people who buy product A also buy product B. Is it necessarily true that 60% of people who buy product B also buy product A?
Yes, because the probabilities must be equal.
No, because this only describes a conditional probability, not the reverse.
Yes, because buying product B makes it more likely someone buys product A.
No, because the probabilities are independent of each other.
How is the marginal probability distribution of X obtained from the joint probability distribution of X and Y?
By multiplying the joint probabilities by the marginal probabilities of Y
By dividing the joint probabilities by the marginal probabilities of Y
By summing the joint probabilities over all possible values of Y
By subtracting the joint probabilities from 1
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?
6/25
4/15
1/6
2/15
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?
5 seconds
14.43 seconds
6.93 seconds
10 seconds
If two random variables X and Y are independent, what can be said about their joint probability distribution?
It cannot be determined from their marginal distributions.
It is equal to the product of their marginal distributions.
It is equal to the sum of their marginal distributions.
It is always a uniform distribution.
The time (in minutes) between customer arrivals at a bank is exponentially distributed with an average of 5 minutes. What is the probability a customer arrives within 3 minutes of the previous customer?
0.368
0.451
0.632
0.549
A fair coin is tossed three times. What is the probability of getting at least two heads?
1/2
1/8
7/8
3/8
In a dataset of customer purchase history, what kind of analysis would likely involve using joint and conditional probability distributions?
Visualizing the distribution of customer ages
Identifying the most frequent purchase day of the week
Calculating the average purchase amount
Predicting the probability of a customer purchasing product B given they purchased product A
Suppose a diagnostic test for a certain disease has a 95% sensitivity and 90% specificity. It means that the test correctly identifies 95% of people with the disease and correctly identifies 90% of people without the disease. If the prevalence of the disease in a population is 1%, what is the probability that a person who tests positive actually has the disease?
0.500
0.095
0.086
0.090
A spam filter correctly identifies 95% of spam emails. However, it also flags 2% of legitimate emails as spam. If 1% of all emails are actually spam, what is the probability that an email flagged as spam is actually spam?
32%
50%
2%
95%