Step-by-step explanation:
Here, the total number of cards in a deck = 52
The total number of heart cards = 13
The total number of red faces in the deck = 6 ( 3 of heart and 3 of diamonds)
Now, out of the TOTAL 6 red face cards, 3 are of hearts.
So, (Red cards) ∩ (Heart cards) = 3 cards ( J, Q and K)
Now let E : Event of picking card which is of heart.
[tex]P(E) = \frac{\textrm{Total number of red hearts}}{\textrm{Total cards}} = \frac{13}{52} = (\frac{1}{4})[/tex]
So, the probability of picking a heart = [tex]\frac{1}{4}[/tex]
Now let F : Event of picking card which is of red face.
[tex]P(E) = \frac{\textrm{Total number of red faces}}{\textrm{Total cards}} = \frac{6}{52} = (\frac{3}{26})[/tex]
So, the probability of picking a red face card = [tex]\frac{3}{26}[/tex]
Hence, the both events E and F are not independent as the intersection of outcomes of both the events is 3 and not equal to [tex]\phi[/tex].
