Answer to Question #159079 in Statistics and Probability for rija

Question

3 Cards are drawn in succession without replacement from an ordinary deck. Find the probability of the event A1 ∩ A2 ∩ A3, where A1 is the event that the first card is RED ace, A2 is the event that the second card Queen or King and A3 is the event that the third card which is greater than 3 and less than Eight ? 

Answer 1

Given

Even + A₁ = All Red cards

Even + A₂ = Queen or King

Even + A₃ = Card greater than 3 and less than eight (4,5,6,7)

52 cards: Red = 26 (13 Diamond, 13 Heart) + Black = 26 (13 Spade, 13 Club)

King (4 cards) → 2 Red, 2 Black

Queen (4 cards) → 2 Red, 2 Black

Jack (4 cards) → 2 Red, 2 Black

Ace (4 cards) → 2 Red, 2 Black

$P(A_1) = \frac{2}{52} \\ P(A_2) = \frac{8}{52} \\ p(A_3) = \frac{4 \times 4 }{52} = \frac{16}{52} \\ P(A_1 \cap A_2 \cap A_3) = 0$

Because no Red Ace card (A₁) lies in the card greater (A₂) than 3 and less than eight and no Ace is King or Queen (A₃). That’s why their intersection will be null.