Compound Probability Math Example 2

Solution

1. 1
   $P(A) = 26/52 = 1/2$ (26 red cards); $P(B) = 12/52 = 3/13$ (12 face cards: J,Q,K in 4 suits)
2. 2
   $P(A \cap B)$ = red face cards: $\{J\heartsuit, Q\heartsuit, K\heartsuit, J\diamondsuit, Q\diamondsuit, K\diamondsuit\} = 6$ cards; $P(A \cap B) = 6/52 = 3/26$
3. 3
   $P(A \cup B) = \frac{1}{2} + \frac{3}{13} - \frac{3}{26} = \frac{13}{26} + \frac{6}{26} - \frac{3}{26} = \frac{16}{26} = \frac{8}{13}$
4. 4
   Check independence: $P(A) \times P(B) = \frac{1}{2} \times \frac{3}{13} = \frac{3}{26} = P(A \cap B)$ → independent