1. The probability the first card is a heart:

A standard deck has 52 cards, with 13 cards from each suit (hearts, diamonds, clubs, and spades). Therefore, the probability that the first card drawn is a heart is the number of heart cards divided by the total number of cards.

So, P(First card is a heart) = 13/52 = 1/4

2. The probability the second card is a red card given the first card was a heart:

If the first card drawn was a heart, then there are now 51 cards left, 25 of which are red (13 diamonds and 12 hearts). So, the probability that the second card is red given that the first was a heart is the number of red cards divided by the total number of remaining cards.

So, P(Second card is red | First card is a heart) = 25/51

3. The probability the first card is a heart and the second card is a red:

The probability that both of these events occur is the product of their individual probabilities. We already calculated these probabilities in the previous steps.

So, P(First card is a heart and second card is red) = P(First card is a heart) * P(Second card is red | First card is a heart) = (1/4) * (25/51) = 25/204

Question

1. The probability the first card is a heart:

A standard deck has 52 cards, with 13 cards from each suit (hearts, diamonds, clubs, and spades). Therefore, the probability that the first card drawn is a heart is the number of heart cards divided by the total number of cards.

So, P(First card is a heart) = 13/52 = 1/4

2. The probability the second card is a red card given the first card was a heart:

If the first card drawn was a heart, then there are now 51 cards left, 25 of which are red (13 diamonds and 12 hearts). So, the probability that the second card is red given that the first was a heart is the number of red cards divided by the total number of remaining cards.

So, P(Second card is red | First card is a heart) = 25/51

3. The probability the first card is a heart and the second card is a red:

The probability that both of these events occur is the product of their individual probabilities. We already calculated these probabilities in the previous steps.

So, P(First card is a heart and second card is red) = P(First card is a heart) * P(Second card is red | First card is a heart) = (1/4) * (25/51) = 25/204

Knowee AI · Accepted Answer

1. The probability the first card is a heart:

A standard deck has 52 cards, with 13 cards from each suit (hearts, diamonds, clubs, and spades). Therefore, the probability that the first card drawn is a heart is the number of heart cards divided by the total number of cards.

So, P(First card is a heart) = 13/52 = 1/4

2. The probability the second card is a red card given the first card was a heart:

If the first card drawn was a heart, then there are now 51 cards left, 25 of which are red (13 diamonds and 12 hearts). So, the probability that the second card is red given that the first was a heart is the number of red cards divided by the total number of remaining cards.

So, P(Second card is red | First card is a heart) = 25/51

3. The probability the first card is a heart and the second card is a red:

The probability that both of these events occur is the product of their individual probabilities. We already calculated these probabilities in the previous steps.

So, P(First card is a heart and second card is red) = P(First card is a heart) * P(Second card is red | First card is a heart) = (1/4) * (25/51) = 25/204

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