Question

4.1 empirical probability. apply the rules of probability. which of the following events has a probability of 1? check all that apply. drawing a red card from a stack of 20 red cards choosing a red marble from a bag containing red and green marbles getting a heads or a tails when flipping a coin drawing a peanut from a bag of trail mix with 4 types of nuts landing on a blue or red space on a spinner with 1 blue space and 1 red space question help: message instructor

Explanation:

Step1: Recall probability formula

Probability $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. A probability of 1 means the event is certain to happen.

Step2: Analyze "drawing a red card from a stack of 20 red cards"

The total number of cards is 20 and the number of red - card (favorable) outcomes is 20. So $P=\frac{20}{20}=1$.

Step3: Analyze "choosing a red marble from a bag containing red and green marbles"

There are non - red (green) marbles, so the probability of choosing a red marble is between 0 and 1, not 1.

Step4: Analyze "getting a heads or a tails when flipping a coin"

When flipping a coin, the only possible outcomes are heads or tails. The number of favorable outcomes (heads or tails) is 2 and the total number of outcomes is 2. So $P = \frac{2}{2}=1$.

Step5: Analyze "drawing a peanut from a bag of trail mix with 4 types of nuts"

There are other types of nuts, so the probability of drawing a peanut is between 0 and 1, not 1.

Step6: Analyze "landing on a blue or red space on a spinner with 1 blue space and 1 red space"

The total number of spaces is 2 (blue + red) and the number of favorable (blue or red) outcomes is 2. So $P=\frac{2}{2}=1$.

Answer:

• drawing a red card from a stack of 20 red cards
• getting a heads or a tails when flipping a coin
• landing on a blue or red space on a spinner with 1 blue space and 1 red space