Question

1. what is the probability of drawing a red card or a face card from a deck, knowing some face cards are also red?

a. \\( \frac { 1 2 } { 5 2 } \\)
b. \\( \frac { 2 0 } { 5 2 } \\)
c. less than \\( \frac { 2 0 } { 5 2 } \\)
d. greater than \\( \frac { 2 0 } { 5 2 } \\)

Explanation:

Step1: Calculate the number of red cards

There are \(26\) red cards (\(13\) hearts and \(13\) diamonds) in a standard deck of \(52\) cards.

Step2: Calculate the number of face cards

There are \(12\) face cards (\(4\) Jacks, \(4\) Queens, \(4\) Kings) in a standard deck.

Step3: Calculate the number of red - face cards

There are \(6\) red - face cards (\(2\) red Jacks, \(2\) red Queens, \(2\) red Kings).

Step4: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Let \(A\) be the event of drawing a red card and \(B\) be the event of drawing a face card.
\(P(A)=\frac{26}{52}\), \(P(B)=\frac{12}{52}\), \(P(A\cap B)=\frac{6}{52}\)
\(P(A\cup B)=\frac{26 + 12-6}{52}=\frac{32}{52}\)
Since \(\frac{32}{52}>\frac{20}{52}\)

Answer:

d. Greater than \(\frac{20}{52}\)