If 2 dice are thrown, then probability that first die shows an even number, and second an odd number, is

Options

A. `1/2`
B. `1/3`
C. `1/4`
D. `1/6`

Answer

To solve the problem of finding the probability that the first die shows an even number and the second die shows an odd number when two dice are thrown, we can follow these steps:

### Step 1: Determine the total number of outcomes when two dice are thrown.
When two dice are thrown, each die has 6 faces. Therefore, the total number of outcomes is calculated as:
\[ \text{Total outcomes} = 6 \times 6 = 36 \]

### Step 2: Identify the favorable outcomes for the first die showing an even number.
The even numbers on a die are 2, 4, and 6. Thus, there are 3 favorable outcomes for the first die:
- 2
- 4
- 6

### Step 3: Identify the favorable outcomes for the second die showing an odd number.
The odd numbers on a die are 1, 3, and 5. Thus, there are 3 favorable outcomes for the second die:
- 1
- 3
- 5

### Step 4: Calculate the number of favorable outcomes for the combined event.
Since the outcomes of the two dice are independent, we can multiply the number of favorable outcomes for the first die by the number of favorable outcomes for the second die:
\[ \text{Favorable outcomes} = 3 \text{ (even outcomes for die 1)} \times 3 \text{ (odd outcomes for die 2)} = 9 \]

### Step 5: Calculate the probability.
The probability of the event is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{9}{36} = \frac{1}{4} \]

### Conclusion:
Thus, the probability that the first die shows an even number and the second die shows an odd number is:
\[ \frac{1}{4} \]