Use the general multiplication rule to find the indicated probability.
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that both cards are black.
A) $\frac { 13 } { 51 }$
B) $\frac { 25 } { 102 }$
C) $\frac { 1 } { 2652 }$
D) $\frac { 25 } { 51 }$

Question

Use the general multiplication rule to find the indicated probability.
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that both cards are black. 
A) $\frac { 13 } { 51 }$
B) $\frac { 25 } { 102 }$
C) $\frac { 1 } { 2652 }$
D) $\frac { 25 } { 51 }$

Quizplus · Accepted Answer

The probability of drawing a black card first is $\frac{26}{52}$ or $\frac{1}{2}$, since half of the 52 cards are black. After drawing one black card, there are now 51 cards left in the deck, with 25 of them being black. Thus, the probability of drawing a second black card is $\frac{25}{51}$. Using the general multiplication rule, the combined probability is $\frac{1}{2} \times \frac{25}{51} = \frac{25}{102}$.

Use the General Multiplication Rule to Find the Indicated Probability 1351\frac { 13 } { 51 }5113​

Use the General Multiplication Rule to Find the Indicated Probability $\frac { 13 } { 51 }$