Question

what is the probability of choosing two consecutive red cards from a standard deck of cards, if replacement is not allowed? possible answers: \\(\frac{51}{100}\\) \\(\frac{61}{204}\\) \\(\frac{23}{25}\\) \\(\frac{25}{102}\\) \\(\frac{17}{25}\\)

Explanation:

Step1: Determine the number of red cards and total cards.

A standard deck has 52 cards, with 26 red cards (hearts and diamonds).

Step2: Calculate the probability of first red card.

The probability of drawing a red card first is $\frac{26}{52}$.

Step3: Calculate the probability of second red card (without replacement).

After drawing one red card, there are 25 red cards left and 51 total cards. So the probability is $\frac{25}{51}$.

Step4: Multiply the two probabilities.

The combined probability is $\frac{26}{52} \times \frac{25}{51} = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102}$.

Answer:

$\frac{25}{102}$ (corresponding to the option with $\frac{25}{102}$)