To find the probability of getting a head and a number greater than 5 when a coin is tossed and a die is rolled:

Step 1: Define the sample spaces

• The coin can result in 2 outcomes: Head (H) or Tail (T).
• The die can result in 6 outcomes: {1, 2, 3, 4, 5, 6}.

Thus, the total number of outcomes when combining both events is:

$2 \times 6 = 12$

Step 2: Favorable outcomes

• A head (H) is one outcome from the coin.
• A number greater than 5 on the die is one of two outcomes: {6}.

Thus, the favorable outcomes are:

• (H, 6)

This is a single outcome.

Step 3: Probability calculation

The probability is the ratio of favorable outcomes to total outcomes:

$P(\text{Head and number > 5}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{12}$

Final Answer:

$\boxed{\frac{1}{12}}$

Would you like further clarification or a different example?

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Related Questions:

1. What is the probability of getting a tail and a number less than 4?
2. What is the probability of getting a head or a number greater than 5?
3. What is the probability of rolling an odd number and flipping a tail?
4. How many total outcomes are possible with a fair coin and an eight-sided die?
5. What is the probability of flipping a coin and rolling a die and both being heads or 6, respectively?

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Tip:

For combined events, always consider the intersection (AND) or union (OR) of events carefully when calculating probabilities!