Find the conditional probability.
-If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart.
A) $\frac { 26 } { 51 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 25 } { 52 }$
D) $\frac { 25 } { 51 }$

Question

Find the conditional probability.
-If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart. 
A) $\frac { 26 } { 51 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 25 } { 52 }$
D) $\frac { 25 } { 51 }$

Quizplus · Accepted Answer

Given that the first card drawn is a heart, it means one red card is already taken out from the deck, leaving 51 cards in total. Since half of a standard deck is red (26 cards) and one red card (a heart) has been removed, there are now 25 red cards left. Therefore, the probability that the second card drawn is red is 25 out of the remaining 51 cards, which is $\frac{25}{51}$.

Find the Conditional Probability 2651\frac { 26 } { 51 }5126​

Find the Conditional Probability $\frac { 26 } { 51 }$