Questions: In a 2-card hand, what is the probability of holding 2 cards of the same suit? Round your answer to three decimal places as needed. A. 0.164 B. 0.200 C. 0.235 D. 0.118

In a 2-card hand, what is the probability of holding 2 cards of the same suit? Round your answer to three decimal places as needed.
A. 0.164
B. 0.200
C. 0.235
D. 0.118

Transcript text: In a 2-card hand, what is the probability of holding 2 cards of the same suit? Round your answer to three decimal places as needed. A. 0.164 B. 0.200 C. 0.235 D. 0.118

Solution

Solution Steps

Step 1: Calculate the Total Number of Ways to Choose 2 Cards from a Deck of 52 Cards

The total number of ways to choose 2 cards from a deck of 52 cards is given by the combination formula: \[ \binom{52}{2} = \frac{52!}{2!(52-2)!} = 1326 \]

Step 2: Calculate the Number of Ways to Choose 2 Cards from the Same Suit

There are 4 suits, and each suit has 13 cards. The number of ways to choose 2 cards from the same suit is: \[ 4 \times \binom{13}{2} = 4 \times \frac{13!}{2!(13-2)!} = 4 \times 78 = 312 \]

Step 3: Calculate the Probability of Drawing 2 Cards of the Same Suit

The probability of drawing 2 cards of the same suit is the ratio of the number of favorable outcomes to the total number of outcomes: \[ \text{Probability} = \frac{312}{1326} \approx 0.2353 \]

Step 4: Round the Probability to Three Decimal Places

Rounding the probability to three decimal places: \[ \text{Rounded Probability} \approx 0.235 \]

Final Answer

The probability of holding 2 cards of the same suit is approximately \(0.235\). Therefore, the answer is: \[ \boxed{0.235} \] The correct option is C.

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