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Magda is playing a game with colored cards. Each card has a number on it. Magda chooses one card at random. All possible outcomes are shown in the table, where each outcome has equal probability.

\begin{tabular}{|c|c|c|c|c|}
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & Red (R) & Green (G) & Yellow (Y) & Blue (B) \\
\hline
1 & R, 1 & G, 1 & Y, 1 & B, 1 \\
\hline
2 & R, 2 & G, 2 & Y, 2 & B, 2 \\
\hline
3 & R, 3 & G, 3 & Y, 3 & B, 3 \\
\hline
\end{tabular}

What is the probability that Magda chooses a card with an even number given that the card is yellow?

A. [tex]$\frac{1}{12}$[/tex]

B. [tex]$\frac{1}{4}$[/tex]

C. [tex]$\frac{1}{3}$[/tex]

D. [tex]$\frac{1}{2}$[/tex]



Answer :

GinnyAnswer
To find the probability that Magda chooses a card with an even number given that the card is yellow, we need to follow a systematic approach.

1. Count the total number of yellow cards:
The table shows the distribution of cards by colors and numbers. Let's identify the yellow cards:
Y, 1 (Yellow card with number 1)
 Y, 2 (Yellow card with number 2)
Y, 3 (Yellow card with number 3)

Therefore, the total number of yellow cards is [tex]\(3\)[/tex].

2. Count the number of yellow cards with an even number:
The table shows that the yellow card with an even number is:
 Y, 2 (Yellow card with number 2)

So, there is exactly [tex]\(1\)[/tex] yellow card with an even number.

3. Calculate the probability:
The probability of choosing a yellow card with an even number given that the card is yellow is the ratio of the number of yellow cards with an even number to the total number of yellow cards.

This can be expressed as:
[tex]\[ \text{Probability} = \frac{\text{Number of yellow cards with an even number}}{\text{Total number of yellow cards}} = \frac{1}{3} \][/tex]

Therefore, the probability that Magda chooses a card with an even number given that the card is yellow is [tex]\(\frac{1}{3}\)[/tex].

So, the correct answer is:
\[ \boxed{\frac{1}{3}}

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