A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. The cards in the deck are placed in random order (usually by a process called `shuffling'). What is the probability that the first two cards drawn from the deck are both red?

Question

A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. The cards in the deck are placed in random order (usually by a process called `shuffling'). What is the probability that the first two cards drawn from the deck are both red?

Answer 1

The correct answer is 25/102.

There are 26 red cards in the set, and 52 cards.
The first card has a
$1/2$ chance of being red and this question is without replacement, meaning it has a dependant equation, and so the next fraction in the equation will be $25/51$.
Now, we multiply $1/2$ and $25/51$, and get $25/102$.

Answer 2

To find the probability that the first two cards drawn from the deck are both red, we need to determine the number of favorable outcomes (drawing two red cards) and the total number of possible outcomes.

The total number of possible outcomes is the number of ways two cards can be drawn from a deck of 52 cards without replacement. When drawing without replacement, the first card drawn reduces the number of available cards for the second draw.

To calculate the number of favorable outcomes (drawing two red cards), we first consider the number of ways to choose the first red card, which is 26 since there are 26 red cards in the deck. After drawing the first red card, there are 25 red cards remaining. For the second draw to also be red, we need to choose one of these remaining 25 red cards.

Therefore, the number of favorable outcomes is 26 * 25, and the total number of possible outcomes is 52 * 51.

The probability is then given by the favorable outcomes divided by the total number of outcomes:

Probability = (Number of favorable outcomes) / (Total number of outcomes).

Plugging in the values, we have:

Probability = (26 * 25) / (52 * 51).

Simplifying this expression, we get:

Probability = 25 / 102.

So, the probability that the first two cards drawn from the deck are both red is 25/102.

Answer 3

(26/52)+(25/51)

Answer 4

No, the second event is dependent on the first, so....

(26/52)(25/51) = .....

Answer 5

I bet Cody meant * not +

Answer 6

its not correct

Answer 7