Conditional Probability

There are 6 possible outcomes when rolling a die, and only one of them is a 6. Therefore, the probability of rolling a 6 is 1/6.

There are 52 cards in a standard deck, and 13 of them are hearts. Therefore, the probability of drawing a heart is 13/52, which simplifies to 1/4.

There are 3 even numbers on a standard six-sided die (2, 4, and 6), and only one of them is a 6. Therefore, the probability of rolling a 6, given that the die has already landed on an even number, is 1/3.

There are 12 face cards in a standard deck of 52 cards, and 3 of them are hearts. Therefore, the probability of drawing a heart, given that the card is a face card, is 3/12, which simplifies to 1/4.

There are 3 numbers greater than 3 on a standard six-sided die (4, 5, and 6), and 2 of them are even (4 and 6). Therefore, the probability of rolling a 6, given that the die has already landed on a number greater than 3, is 2/3.

There are 26 red cards in a standard deck of 52 cards, and 13 of them are hearts. Therefore, the probability of drawing a heart, given that the card is a red card, is 13/26, which simplifies to 1/2.

There are 4 numbers that are not multiples of 3 on a standard six-sided die (1, 2, 4, and 5), and 2 of them are even (2 and 4). Therefore, the probability of rolling a 6, given that the die has already landed on a number that is not a multiple of 3, is 2/4, which simplifies to 1/2.

There are no hearts in a standard deck of 52 cards that are black. Therefore, the probability of drawing a heart, given that the card is a black card, is 0.

There are 5 numbers that are not multiples of 2 on a standard six-sided die (1, 3, 4, 5, and 6), and 2 of them are even (4 and 6). Therefore, the probability of rolling a 6, given that the die has already landed on a number that is not a multiple of 2, is 2/5.

There are no hearts in a standard deck of 52 cards that are clubs. Therefore, the probability of drawing a heart, given that the card is a club, is 0.

There are 4 numbers that are not multiples of 4 on a standard six-sided die (1, 2, 3, and 5), and 2 of them are even (2 and 4). Therefore, the probability of rolling a 6, given that the die has already landed on a number that is not a multiple of 4, is 2/4, which simplifies to 1/2.

There are no hearts in a standard deck of 52 cards that are diamonds. Therefore, the probability of drawing a heart, given that the card is a diamond, is 0.

There are 5 numbers that are not multiples of 5 on a standard six-sided die (1, 2, 3, 4, and 6), and 2 of them are even (2 and 4). Therefore, the probability of rolling a 6, given that the die has already landed on a number that is not a multiple of 5, is 2/5.

There are no hearts in a standard deck of 52 cards that are spades. Therefore, the probability of drawing a heart, given that the card is a spade, is 0.

There are 5 numbers that are not multiples of 6 on a standard six-sided die (1, 2, 3, 4, and 5), and 2 of them are even (2 and 4). Therefore, the probability of rolling a 6, given that the die has already landed on a number that is not a multiple of 6, is 2/5.