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

Solution Steps

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

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

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: \[ \text{Probability} = \frac{312}{1326} \approx 0.2353 \]

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

Final Answer