List of top Mathematics Questions on Independent Events asked in CBSE Class XII

If \(E\) and \(F\) are two independent events such that \[ P(E)=\frac{3}{10}, \qquad P(E\cup F)=\frac{1}{2}, \] then \[ P(E|F)-P(F|E) \] is equal to: 

The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed.
The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
A box contains 6 cards numbered 1 to 6. A student is asked to pick up two cards, one by one after replacement and note down the numbers on the cards. Let A be the event of getting sum of the numbers on two cards as 10, and B, the event of a number other than 4 on the first card selected. Find \( P(A \text{ and } B) \) and find whether the events A and B are independent events or not.
A box contains 6 cards numbered 1 to 6. A student is asked to pick up two cards, one by one after replacement and note down the numbers on the cards. Let A be the event of getting sum of the numbers on two cards as 10, and B, the event of a number other than 4 on the first card selected.
Find P(A and B) and find whether the events A and B are independent events or not.
If \(E\) and \(F\) are two independent events such that \[ P(E)=\frac{3}{10}, \qquad P(E\cup F)=\frac{1}{2}, \] then \[ P(E\mid F)-P(F\mid E) \] is equal to \[ \_\_\_\_. \]