Question

question 12: for each row, determine the probability of drawing the card or type of card shown. assume that the card is drawn from a shuffled deck of standard playing cards. round decimals to the nearest thousandth and percents to the nearest tenth of a percent.

	probability as a fraction	probability as a decimal	probability as a percentage
p(club)
p(5 or 10)

Explanation:

Part 1: \( P(\text{Ace}) \)

Step 1: Determine number of Aces and total cards

A standard deck has 4 Aces and 52 total cards. Probability formula: \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)
So, \( P(\text{Ace}) = \frac{4}{52} = \frac{1}{13} \)

Step 2: Convert to decimal

\( \frac{1}{13} \approx 0.077 \) (rounded to nearest thousandth)

Step 3: Convert to percentage

\( 0.077 \times 100 = 7.7\% \) (rounded to nearest tenth of a percent)

Part 2: \( P(\text{Club}) \)

Step 1: Determine number of Clubs and total cards

A standard deck has 13 Clubs and 52 total cards.
So, \( P(\text{Club}) = \frac{13}{52} = \frac{1}{4} \)

Step 2: Convert to decimal

\( \frac{1}{4} = 0.250 \)

Step 3: Convert to percentage

\( 0.250 \times 100 = 25.0\% \)

Part 3: \( P(5 \text{ or } 10) \)

Step 1: Determine number of 5s, 10s, and total cards

There are 4 fives and 4 tens, so total favorable outcomes: \( 4 + 4 = 8 \). Total cards: 52.
Thus, \( P(5 \text{ or } 10) = \frac{8}{52} = \frac{2}{13} \)

Step 2: Convert to decimal

\( \frac{2}{13} \approx 0.154 \) (rounded to nearest thousandth)

Step 3: Convert to percentage

\( 0.154 \times 100 = 15.4\% \) (rounded to nearest tenth of a percent)

Final Table (Filled):

	Probability as a fraction	Probability as a decimal	Probability as a percentage
\( P(\text{Club}) \)	\( \frac{1}{4} \)	\( 0.250 \)	\( 25.0\% \)
\( P(5 \text{ or } 10) \)	\( \frac{2}{13} \)	\( 0.154 \)	\( 15.4\% \)

Answer:

Part 1: \( P(\text{Ace}) \)

Step 1: Determine number of Aces and total cards

A standard deck has 4 Aces and 52 total cards. Probability formula: \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)
So, \( P(\text{Ace}) = \frac{4}{52} = \frac{1}{13} \)

Step 2: Convert to decimal

\( \frac{1}{13} \approx 0.077 \) (rounded to nearest thousandth)

Step 3: Convert to percentage

\( 0.077 \times 100 = 7.7\% \) (rounded to nearest tenth of a percent)

Part 2: \( P(\text{Club}) \)

Step 1: Determine number of Clubs and total cards

A standard deck has 13 Clubs and 52 total cards.
So, \( P(\text{Club}) = \frac{13}{52} = \frac{1}{4} \)

Step 2: Convert to decimal

\( \frac{1}{4} = 0.250 \)

Step 3: Convert to percentage

\( 0.250 \times 100 = 25.0\% \)

Part 3: \( P(5 \text{ or } 10) \)

Step 1: Determine number of 5s, 10s, and total cards

There are 4 fives and 4 tens, so total favorable outcomes: \( 4 + 4 = 8 \). Total cards: 52.
Thus, \( P(5 \text{ or } 10) = \frac{8}{52} = \frac{2}{13} \)

Step 2: Convert to decimal

\( \frac{2}{13} \approx 0.154 \) (rounded to nearest thousandth)

Step 3: Convert to percentage

\( 0.154 \times 100 = 15.4\% \) (rounded to nearest tenth of a percent)

Final Table (Filled):

	Probability as a fraction	Probability as a decimal	Probability as a percentage
\( P(\text{Club}) \)	\( \frac{1}{4} \)	\( 0.250 \)	\( 25.0\% \)
\( P(5 \text{ or } 10) \)	\( \frac{2}{13} \)	\( 0.154 \)	\( 15.4\% \)