Question

assume that 2 cards are drawn from a standard 52 - card deck. find the following probabilities.
a) assume the cards are drawn without replacement. find the probability of drawing 2 black cards.
b) assume the cards are drawn with replacement. find the probability of drawing 2 black cards.
a. the probability of drawing 2 black cards without replacement is \\( \square \\).
(simplify your answer.)

Explanation:

Step1: Calculate the probability of drawing the first black card

In a standard 52 - card deck, there are 26 black cards.
The probability of drawing the first black card \(P(B_1)=\frac{26}{52}\)

Step2: Calculate the probability of drawing the second black card without replacement

After drawing one black card, there are 25 black cards left and 51 cards in total.
The probability of drawing the second black card \(P(B_2|B_1)=\frac{25}{51}\)

Step3: Use the multiplication rule for dependent events

The probability of drawing 2 black cards without replacement \(P = P(B_1)\times P(B_2|B_1)\)

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Answer:

\(\frac{25}{102}\)