4. a die is rolled, and a penny is dropped. find the probability of rolling a two and showing a tail.
4. a die is rolled, and a penny is dropped. find the probability of rolling a two and showing a tail.
Answer
Explanation:
Step1: Determine probability of rolling a 2
A die has 6 faces. The probability of rolling a 2 is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 2) out of 6 possible outcomes.
Step2: Determine probability of getting a tail
A penny has 2 sides. The probability of getting a tail is $\frac{1}{2}$ since there is 1 favorable outcome (tail) out of 2 possible outcomes.
Step3: Use multiplication rule for independent events
Since rolling a die and dropping a penny are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = \frac{1}{6}\times\frac{1}{2}=\frac{1}{12}$.
Answer:
$\frac{1}{12}$