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?
[2]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?
[3]Three fair coins are flipped. Given that at least one coin shows heads, what is the probability that all three are heads?
[3]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?
[4]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?
[4]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?
[5]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?
[3]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?
[4]A fair coin is flipped three times. Given that exactly two heads occur, what is the probability that the first flip was a head?
[3]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?
[5]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?
[3]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?
[2]