Question

• independent events •

two events are considered independent if the occurrence of one event does not affect the probability of the other event.
flipping a heads and flipping a tails are independent events because flipping a heads does not affect the probability of flipping a tails, and vice versa. the probability of flipping a heads or a tails will always be $\frac{1}{2}$.
drawing a heart and rolling a six are independent events because drawing a heart does not affect the probability of rolling a six, and vice versa.
try these: determine whether or not the events are independent.

1. rolling a die and flipping a coin. yes / no
2. drawing a marble from a bag and then drawing another without replacing the first. yes / no
3. drawing a heart and then drawing a club from the remaining cards. yes / no
4. flipping a coin twice. yes / no
5. rolling a die and spinning a spinner. yes / no

Explanation:

Step1: Recall independent - events definition

Two events are independent if the occurrence of one does not affect the probability of the other.

Step2: Analyze event 1

Rolling a die has no impact on flipping a coin. So, they are independent.

Step3: Analyze event 2

When drawing a marble without replacement, the first - draw affects the second - draw probabilities. So, they are dependent.

Step4: Analyze event 3

Drawing a heart first changes the number of remaining cards, affecting the probability of drawing a club. So, they are dependent.

Step5: Analyze event 4

The first coin - flip does not affect the second coin - flip. So, they are independent.

Step6: Analyze event 5

Rolling a die has no influence on spinning a spinner. So, they are independent.

Answer:

1. YES
2. NO
3. NO
4. YES
5. YES