For any two events A and B in sample space S, which of the following options is NOT true?
P(A | B) = P(B | A)
(\( P(A|S) = P(A) \)) is true because conditioning on the entire sample space \( S \) does not change the probability of \( A \).
\[ P(A|S) = \frac{P(A \cap S)}{P(S)} = \frac{P(A)}{1} = P(A) \]
(\( P(A|B) = P(B|A) \)) is false in general. This equality only holds if \( P(A) = P(B) \).
\[ P(A|B) = \frac{P(A \cap B)}{P(B)}, \quad P(B|A) = \frac{P(A \cap B)}{P(A)} \]
(\( A \) and \( \emptyset \) are independent) is true because \( P(A \cap \emptyset) = P(A)P(\emptyset) = 0 \).
(\( A \) and \( S \) are independent) is true because \( P(A \cap S) = P(A) = P(A)P(S) \).
Similar Questions
If A and B are two events such that P(A∪B) = 3/4 P(A∩B)
Suppose a die is thrown four times and 5, 3, 5, 3 are obtained, respectively. Then the empirical probability of getting 5 is:
If a biased coin is tossed 10 times, out of which head is obtained 3 times, then what is the probability of getting head on the 11th toss?
Find the probability that there may be 53 Sundays in a leap year.
25 books are placed at random on a shelf. The probability that a particular pair of books shall be always together is:
On rolling of a die, the events E1 (getting an even number) and E2 (getting an odd number) are:
If a fair six-sided die is tossed twice and the tosses are independent, then the probability of getting a 5 on both tosses is:
Die I has 4 red and 2 white faces and die II has 2 red and 4 white faces. A coin is flipped once. If head appears, the game continues by flipping die I, and if tail appears, then die II is used. The probability of getting a red face at any throw is:
As the sample size increases, empirical probability:
'p' is the probability that a man aged x years will die in a year. A man aged x, A₁ will die in a year and will be the first to die.
Important Questions from Probability
Two dice are thrown simultaneously. What is the probability of getting the same number on both the dice?
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
When two dice are tossed simultaneously, the probability that the sum of the numbers appearing on both the dice is 8 will be
