What is an example of two events that are neither disjoint nor independent?
(I have no idea how that would even work)
throwing 2 dice and flipping a coin.
suppose you want the prob(heads and a sum of 7)
the process of flipping the coin has no effect on the act of throwing the dice.
Thus the events are "independent"
sorry I misread your question
If the sets are not disjoint then they have elements in common.
for example
the set A containing numbers 1 through 7. There is only one of each number in the set.I can only pick from set A
and
the set B containing numbers 6 through 9. There is only one of each number in the set. You can only pick from set B
Is the probability of picking a number from set B changed by the previous random selection of a number from box A?
Sure it is. If I took the six or the seven from set A, I took it from the intersection, and you can not pick it. Therefore the events are not independent.
To find an example of two events that are neither disjoint nor independent, we need to understand what these terms mean.
1. Disjoint events: Disjoint events, also known as mutually exclusive events, are events that cannot happen at the same time. In other words, if one event occurs, the other event cannot occur, and vice versa.
2. Independent events: Independent events are events where the occurrence of one event does not affect the occurrence of the other. In other words, the probability of both events occurring is equal to the product of their individual probabilities.
Now, let's find an example of two events that are neither disjoint nor independent. Consider rolling a fair six-sided die.
Event A: Getting an even number (2, 4, or 6)
Event B: Getting a prime number (2, 3, or 5)
These events are not disjoint since the number 2 is common to both events. If we roll a 2, it satisfies both Event A and Event B simultaneously.
These events are also not independent because the occurrence of Event A affects the probability of Event B. Since Event A has occurred (we rolled an even number), the probability of getting a prime number (Event B) has changed. After getting an even number, the only possible prime number is 2; therefore, the probability has reduced.
Hence, Event A and Event B are an example of two events that are neither disjoint nor independent.