Question:medium

A and B are independent events of a random experiment if and only if:

Show Hint

For two events to be independent, the probability of one event occurring should not change based on the occurrence of the other event. Therefore, conditional probabilities should remain constant regardless of the event.
Updated On: Jan 13, 2026
  • \( P(A | B) \neq P(A \cap B) \)
  • \( P(A | B) = P(B | A) \)
  • \( P(A | B) \neq P(A | B^c) \)
  • \( P(A | B) = P(A | B^c) \)
Show Solution

The Correct Option is D

Solution and Explanation

Events \(A\) and \(B\) are independent if the occurrence of one does not influence the probability of the other. Mathematically, this is expressed as:\[P(A | B) = P(A) \quad \text{and} \quad P(B | A) = P(B).\]Using conditional probabilities, the condition for event independence is:\[P(A | B) = P(A) \quad \text{which also means} \quad P(A | B) = P(A | B^c).\]Therefore, the correct option is \(\boxed{(d)}\).
Was this answer helpful?
0

Top Questions on Relations and functions

Questions Asked in VITEEE exam

Read the passage carefully and choose the best answer to each question out of the four alternatives.
“People very often complain that poverty is a great evil and that it is not possible to be happy unless one has a lot of money. Actually, this is not necessarily true. Even a poor man, living in a small hut with none of the comforts and luxuries of life, may be quite contented with his lot and achieve a measure of happiness. On the other hand, a very rich man, living in a palace and enjoying everything that money can buy, may still be miserable, if, for example, he does not enjoy good health or his only son has taken to evil ways. Apart from this, he may have a lot of business worries which keep him on tenterhooks most of the time. There is a limit to what money can buy and there are many things which are necessary for a man’s happiness and which money cannot procure. Real happiness is a matter of the right attitude and the capacity of being contented with whatever you have is the most important ingredient of this attitude.”
View Solution