Question Type 5: Working with conditions Bootcamps

From a standard 52-card deck, two cards are drawn at random without replacement. Given that the first card is red, what is the probability that the second card is also red?

A single card is drawn from a standard 52-card deck. Given that it is a face card, what is the probability that it is a heart?

A fair coin is flipped three times. Given that exactly two heads occur, what is the probability that the first flip was a head?

Three fair coins are flipped. Given that at least one coin shows heads, what is the probability that all three are heads?

Two fair six-sided dice are rolled. Given that the sum of the two dice is even, what is the probability that the sum is greater than 9?

Two fair six-sided dice are rolled. Given that the sum is a multiple of 3, what is the probability that both dice show the same number?

An urn contains 5 red and 7 blue balls. Two balls are drawn at random without replacement. Given that the second ball drawn is red, what is the probability that the first ball drawn was blue?

An urn contains 4 white and 6 black balls. A ball is drawn and replaced three times. Given that exactly two of the three draws are white, what is the probability that the first draw was white?

Two fair six-sided dice are rolled. Given that the first die shows a number greater than the second die, what is the probability that the sum of the two dice is 8?

Two fair six-sided dice are rolled. Given that at least one die shows a 5, what is the probability that the sum of the dice is 9?

Two fair dice are rolled. Given that at least one die shows a 6, what is the probability that the sum of the dice is 8?

Three fair six-sided dice are rolled. Given that the maximum of the three rolls is 5, what is the probability that the minimum roll is 3?