type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction…
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?
Answer
Explanation:
Step1: Probability of rolling a five
A six - sided die has 6 possible outcomes. Rolling a five is 1 outcome. So the probability is $\frac{1}{6}$.
Step2: Probability of flipping a coin and getting heads
A coin has 2 possible outcomes (heads or tails). Getting heads is 1 outcome. So the probability is $\frac{1}{2}$.
Step3: Probability of rolling a five and getting heads
Since the events are independent, we multiply the probabilities of each event. So it is $\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}$.
Step4: Determine independence
The outcome of rolling a die does not affect the outcome of flipping a coin and vice - versa. So the events are independent.
Answer:
$\frac{1}{6}$ $\frac{1}{2}$ $\frac{1}{12}$ Independent