Answer:
[tex]\frac{1}{13}[/tex]
Step-by-step explanation:
Given: A single card is drawn from a standard deck of cards.
To find: P(queen | black)
Solution:
Probability refers to chances of occurrence of any event.
Use the formula: P(A | B) = P(A∩B) ÷ P(B)
Let A denotes the event that the card drawn is queen.
Let B denotes the event that the card drawn is black.
Total number of cards = 52
Probability = Number of favorable outcomes ÷ Total number of possible outcomes
P(queen ∩ black) = P(card drawn is black and queen)
= [tex]\frac{2}{52}=\frac{1}{26}[/tex]
P(black) [tex]=\frac{26}{52}=\frac{1}{2}[/tex]
Therefore,
P(queen | black) = P(queen ∩ black) ÷ P(black)
= [tex]\frac{\frac{1}{26} }{\frac{1}{2} }=\frac{2}{26}=\frac{1}{13}[/tex]
