Answer:
[tex]\sf F. \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
A deck of 52 playing cards contains 13 hearts.
If Sara has 12 cards from this deck in her hand and 3 of them are hearts, then:
Total cards remaining in the deck
= total deck - cards Sara has
= 52 - 12
= 40
Total hearts left in the remaining deck
= total heart cards - heart cards Sara has
= 13 - 3
= 10
So there are 40 cards in the deck and 10 of them are hearts.
Probability Formula[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore, the probability that a card drawn at random from the remainder of the deck will be a heart is:
[tex]\begin{aligned}\implies \sf P(heart) & =\dfrac{\textsf{number of hearts in remaining deck}}{\textsf{total cards in remaining deck}}\\\\ & =\dfrac{10}{40}\\ \\& =\dfrac{1}{4}\end{aligned}[/tex]
