Question

The probability that Terri will draw a heart and then a red face card from a standard 52-card deck is . Using this probability, determine if the event of drawing a heart and the event of drawing a red face card was independent, dependent, both, or neither.

Answer 1

The both events are not independent as the intersection of outcomes of both the events is 3  and  not equal to Ф.

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.

$P(E) = \frac{\textrm{Total number of red hearts}}{\textrm{Total cards}} = \frac{13}{52} = (\frac{1}{4})$

So, the probability of picking a heart = $\frac{1}{4}$

Now let F : Event of picking card which is of red face.

$P(E) = \frac{\textrm{Total number of red faces}}{\textrm{Total cards}} = \frac{6}{52} = (\frac{3}{26})$

So, the probability of picking a red face card  = $\frac{3}{26}$

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 $\phi$.