Question

41 fill in the blank 3 points 1 card is drawn from a standard deck of 52 playing cards. find the probability of drawing a king. round your answer to three decimal places. type your answer... find the probability of drawing a king or jack. round your answer to three decimal places. type your answer... find the probability of drawing a king or spade. round your answer to three decimal places. type your answer...

Explanation:

Step1: Calculate probability of drawing a King

There are 4 Kings in a 52 - card deck. Probability formula: \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the total number of outcomes. So \(P(\text{King})=\frac{4}{52}=\frac{1}{13}\approx0.077\)

Step2: Calculate probability of drawing a King or Jack

There are 4 Kings and 4 Jacks. Using the formula \(P(A\cup B)=\frac{n(A)+n(B)}{n(S)}\) (since King and Jack are mutually - exclusive events). \(n(A) = 4\) (Kings), \(n(B)=4\) (Jacks), \(n(S) = 52\). So \(P(\text{King or Jack})=\frac{4 + 4}{52}=\frac{8}{52}=\frac{2}{13}\approx0.154\)

Step3: Calculate probability of drawing a King or Spade

There are 4 Kings and 13 Spades. But the King of Spades is counted twice. Using the formula \(P(A\cup B)=\frac{n(A)+n(B)-n(A\cap B)}{n(S)}\). \(n(A) = 4\) (Kings), \(n(B)=13\) (Spades), \(n(A\cap B) = 1\) (King of Spades), \(n(S)=52\). So \(P(\text{King or Spade})=\frac{4+13 - 1}{52}=\frac{16}{52}=\frac{4}{13}\approx0.308\)

Answer:

0.077
0.154
0.308