Graph the inequalities y <= x and y <= 1 - x. Both of these are regions in the plane. The graphs should show you whether events A and B are independent.atrus_ovis said:Homework Statement
0<=x<=1 0<=,y <=1
event A: y<=x
event B: y<=1-x
Are events A,B independent?
Also, if B: x<=1/4 , are A,B independent?
The Attempt at a Solution
if independent,
P(A|B) = P(A)
P(A|B) = P(A)P(B) / P(A)P(B)+(1-P(A))P(B)
... ?
For B: x<=1/4 they are obviously dependent, as B normalizes the event space to the part
where x<=1/4, thus affecting the probability of A, since it involves x.
I can't express it mathematically though, in the formula.
The "event independence little problem" refers to a phenomenon in which the occurrence of one event does not affect the probability of another event happening. This is also known as the "independence of events" or the "independence assumption" in probability theory.
Event independence is determined by analyzing the relationship between the events in question. If the probability of one event occurring remains the same regardless of whether or not the other event occurs, then the events are considered to be independent.
Examples of event independence include flipping a coin and rolling a die. The outcome of one event (flipping a coin) does not affect the outcome of the other event (rolling a die). Another example is drawing two cards from a deck without replacement. The probability of drawing a certain card does not change based on whether or not another card was previously drawn.
Event independence is an important concept in probability calculations because it allows for simpler and more accurate calculations. When events are independent, the probability of the events both occurring is simply the product of the individual probabilities. For example, the probability of getting heads on a coin flip and rolling a 4 on a die is (1/2)*(1/6) = 1/12.
No, events cannot be both independent and dependent at the same time. Independence means that the occurrence of one event does not affect the probability of another event happening, while dependence means that the occurrence of one event does affect the probability of another event happening. However, events can be conditionally independent, meaning they are independent under certain conditions but not independent under others.