Question

jenelle draws one card from a standard deck of 52 cards. determine the probability of drawing either a two or a king? write your answer as a reduced fraction. answer = determine the probability of drawing either a two or a spade? write your answer as a reduced fraction. answer =

Explanation:

Step1: Calculate probability for two or king

• Number of twos in a deck: \(4\)
• Number of kings in a deck: \(4\)
• Use the formula \(P(A\cup B)=P(A)+P(B)\) (since \(A\) (drawing a two) and \(B\) (drawing a king) are mutually - exclusive events, \(P(A\cap B) = 0\))
• \(P(\text{two or king})=\frac{4 + 4}{52}=\frac{8}{52}=\frac{2}{13}\)

Step2: Calculate probability for two or spade

• Number of twos: \(4\)
• Number of spades: \(13\)
• Number of two of spades (overlap): \(1\)
• Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
• \(P(\text{two or spade})=\frac{4+13 - 1}{52}=\frac{16}{52}=\frac{4}{13}\)

Answer:

\(\frac{2}{13}\)
\(\frac{4}{13}\)