Question

what is the probability of rolling 4 and flipping heads? the probability of rolling 4 and flipping heads is \\(\frac{\square}{\square}\\).

Explanation:

Step1: Probability of rolling 4

A die has 6 faces (1 - 6). The probability of rolling a 4 is the number of favorable outcomes (1, since only 4 is desired) divided by total outcomes (6). So, \( P(\text{roll 4})=\frac{1}{6} \).

Step2: Probability of flipping heads

A coin has 2 sides (heads, tails). The probability of flipping heads is the number of favorable outcomes (1) divided by total outcomes (2). So, \( P(\text{flip heads})=\frac{1}{2} \).

Step3: Probability of both events (independent)

Since rolling a die and flipping a coin are independent events, the probability of both occurring is the product of their individual probabilities. So, \( P(\text{roll 4 and flip heads}) = P(\text{roll 4}) \times P(\text{flip heads})=\frac{1}{6} \times \frac{1}{2}=\frac{1}{12} \).

Answer:

\(\frac{1}{12}\)