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. greater than
b.
c. less than
d.

Explanation:

Step1: Calculate the number of red cards, face cards and red - face cards

• A standard deck has \(n = 52\) cards.
• Number of red cards \(n(R)=26\) (13 hearts and 13 diamonds).
• Number of face cards \(n(F)=12\) (4 Jacks, 4 Queens, 4 Kings).
• Number of red - face cards \(n(R\cap F) = 6\) (2 red Jacks, 2 red Queens, 2 red Kings).

Step2: Use the formula for the probability of the union of two events

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
Here, \(P(R\cup F)=\frac{n(R)}{n}+\frac{n(F)}{n}-\frac{n(R\cap F)}{n}\).
Substitute the values: \(\frac{26}{52}+\frac{12}{52}-\frac{6}{52}=\frac{26 + 12-6}{52}=\frac{32}{52}=\frac{8}{13}\approx0.615\).
Since \(\frac{8}{13}\approx0.615\) and \(\frac{6}{13}\approx0.462\), \(\frac{8}{13}>\frac{6}{13}\).

Answer:

A. Greater than \(\frac{6}{13}\)