Conditional Probability

Bag I contains 4 white and 6 black balls. Bag II contains 4 white and 3 black balls. One ball is drawn at random from any one of the two bags and it is found to be a black ball. Th...

Given that A and B are not null sets, which of the following statements regarding probability is/are CORRECT?

Given that $A$ and $B$ are not null sets, which of the following statements regarding probability is/are CORRECT?

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having...

In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having...

Four cards are randomly selected from a pack of $$52$$ cards. If the first two cards are kings, what is the probability that the third card is a king?

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Given that gate $$1$$ has failed, the probability that both ga...