A coin and a die are tossed . Describe the following events .
B : getting a prime number ,

Answer

To solve the problem of describing the event B: getting a prime number when a coin and a die are tossed, we can follow these steps:

### Step 1: Identify the Sample Space
When a coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When a die is tossed, there are six possible outcomes: 1, 2, 3, 4, 5, and 6.

Thus, the sample space (S) for tossing a coin and a die can be represented as:
\[ S = \{ (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) \} \]

### Step 2: Identify Prime Numbers
Next, we need to identify the prime numbers from the outcomes of the die. The prime numbers less than or equal to 6 are:
- 2
- 3
- 5

### Step 3: Describe Event B
Now, we will describe the event B, which is getting a prime number when the coin and die are tossed.

Event B can occur in the following combinations:
- If the coin shows Heads (H):
- (H, 2)
- (H, 3)
- (H, 5)

- If the coin shows Tails (T):
- (T, 2)
- (T, 3)
- (T, 5)

Thus, the event B can be represented as:
\[ B = \{ (H, 2), (H, 3), (H, 5), (T, 2), (T, 3), (T, 5) \} \]

### Step 4: Conclusion
The event B consists of 6 outcomes where a prime number is rolled on the die, regardless of whether the coin shows heads or tails.

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