sasha is working on a magic trick with a standard deck of cards. she chooses an ace, puts it back, then…

sasha is working on a magic trick with a standard deck of cards. she chooses an ace, puts it back, then chooses a red card. what is $p(\\text{ace}|\\text{red})$? round to the nearest tenth. (1 point)

sasha is working on a magic trick with a standard deck of cards. she chooses an ace, puts it back, then chooses a red card. what is $p(\\text{ace}|\\text{red})$? round to the nearest tenth. (1 point)

Answer

Explanation:

Step1: Determine number of red cards and red aces

A standard deck has 52 cards, 26 red cards (13 hearts and 13 diamonds), and 2 red aces (ace of hearts and ace of diamonds).

Step2: Use conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of equally - likely outcomes, $P(\text{ace}|\text{red})=\frac{n(\text{ace and red})}{n(\text{red})}$, where $n$ is the number of elements in the set. Here, $n(\text{ace and red}) = 2$ and $n(\text{red})=26$. So $P(\text{ace}|\text{red})=\frac{2}{26}=\frac{1}{13}\approx 0.077$. To convert to a percentage, we multiply by 100: $0.077\times100 = 7.7%$. Rounding to the nearest tenth, we get $7.7%$.

Answer:

$7.7%$