Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar. brenda is rolling a six - sided die and flipping a coin. complete each of the following sentences regarding the probabilities involved in these actions using reduced fractions. the probability of rolling a five is. the probability of flipping the coin and it landing on heads is. the probability of rolling a five and landing on heads is. are the events independent or dependent?

Explanation:

Step1: Calculate die roll probability

A 6-sided die has 1 favorable outcome (rolling a 5) out of 6 total outcomes.
Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{6}$

Step2: Calculate coin flip probability

A coin has 1 favorable outcome (heads) out of 2 total outcomes.
Probability = $\frac{1}{2}$

Step3: Calculate combined probability

For independent events, multiply individual probabilities.
Probability = $\frac{1}{6} \times \frac{1}{2} = \frac{1}{12}$

Step4: Classify event dependence

Rolling a die and flipping a coin do not affect each other, so they are independent.

Answer:

The probability of rolling a five is $\frac{1}{6}$
The probability of flipping the coin and it landing on heads is $\frac{1}{2}$
The probability of rolling a five and landing on heads is $\frac{1}{12}$
Are the events independent or dependent? independent