Answer:
Option 4) Probability = 30%
Step-by-step explanation:
We are given the following information:
We have a deck of cards.
We have to find the probability of drawing a face card given that is a heart.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
Conditional probability:
The probability of happening of event A given event B:
[tex]P(A|B) = \displaystyle\frac{P(A \cap B)}{P(B)}[/tex]
[tex]P(\text{Face card}|\text{Hearts}) = \displaystyle\frac{P(\text{Face card} \cap \text{Hearts})}{P(\text{Hearts)}}\\P(\text{Hearts}) = \displaystyle\frac{13}{52}\\\\P(\text{Face card} \cap \text{Hearts}) = \frac{4}{52}\\\\P(\text{Face card}|\text{Hearts}) = \frac{4/52}{13/52} = \frac{4}{13}\\\\=\frac{4}{13}\times 100\% = 30.77\%[/tex]
