If 2 cards are drawn from a pack of 52, then probability that they are from the same suit is

Options

A. `4/7`
B. `4/17`
C. `3/17`
D. `4/13`

Answer

To find the probability that two cards drawn from a pack of 52 cards are from the same suit, we can follow these steps:

### Step 1: Determine the Total Number of Ways to Draw 2 Cards
The total number of ways to choose 2 cards from 52 can be calculated using the combination formula:

\[ \text{Total ways} = \binom{52}{2} = \frac{52 \times 51}{2} = 1326 \]

### Step 2: Determine the Number of Favorable Outcomes
Next, we need to find the number of ways to draw 2 cards from the same suit. There are 4 suits (hearts, diamonds, clubs, and spades), and each suit has 13 cards.

1. **Choose a suit**: There are 4 ways to choose a suit.
2. **Choose 2 cards from that suit**: For each suit, the number of ways to choose 2 cards from 13 is:

\[ \binom{13}{2} = \frac{13 \times 12}{2} = 78 \]

So, the total number of favorable outcomes is:

\[ \text{Favorable outcomes} = 4 \times 78 = 312 \]

### Step 3: Calculate the Probability
The probability that the two cards drawn are from the same suit is given by the ratio of favorable outcomes to total outcomes:

\[ P(\text{same suit}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{312}{1326} \]

### Step 4: Simplify the Probability
Now, we simplify the fraction:

\[ \frac{312}{1326} = \frac{4}{17} \]

Thus, the probability that the two cards drawn are from the same suit is:

\[ \boxed{\frac{4}{17}} \]

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