A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is

Options

A. `1/2`
B. `1/4`
C. `1/8`
D. `3/4`

Answer

To solve the problem step by step, we need to find the probability of two independent events: rolling an even number on a die and drawing a spade from a deck of cards.

### Step-by-Step Solution:

**Step 1: Determine the probability of rolling an even number on a die.**

A standard die has six faces numbered from 1 to 6. The even numbers on a die are 2, 4, and 6.

- Total outcomes when rolling a die = 6 (1, 2, 3, 4, 5, 6)
- Favorable outcomes for even numbers = 3 (2, 4, 6)

The probability of rolling an even number (Event A) is given by:

\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} \]

**Step 2: Determine the probability of drawing a spade from a deck of cards.**

A standard deck of playing cards has 52 cards, which includes 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards.

- Total outcomes when drawing a card = 52
- Favorable outcomes for drawing a spade = 13

The probability of drawing a spade (Event B) is given by:

\[ P(B) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{13}{52} = \frac{1}{4} \]

**Step 3: Calculate the combined probability of both events occurring.**

Since the two events (rolling a die and drawing a card) are independent, the probability of both events occurring together is the product of their individual probabilities:

\[ P(A \text{ and } B) = P(A) \times P(B) = \frac{1}{2} \times \frac{1}{4} \]

Calculating this gives:

\[ P(A \text{ and } B) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \]

### Final Answer:
The probability of getting an even number on the die and a spade card is \(\frac{1}{8}\).

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