Question

which of the following events has a probability of 1? choose three correct answers.
drawing a peanut from a bag of trail mix with 4 types of nuts
choosing a red marble from a bag containing red and green marbles
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

Explanation:

Step1: Analyze the probability of each event

• Event 1: drawing a peanut from a bag of trail mix with 4 types of nuts

The probability is $\frac{1}{4}$ since there are 4 types of nuts and we are interested in 1 type (peanuts).

• Event 2: choosing a red marble from a bag containing red and green marbles

Let the number of red marbles be $r$ and green marbles be $g$. The probability is $\frac{r}{r + g}$, which is less than 1 unless $g = 0$ (but the problem doesn't state that).

• Event 3: drawing a red card from a stack of 20 red cards

All 20 cards are red. So the probability of drawing a red card is $\frac{20}{20}=1$.

• Event 4: getting a heads or a tails when flipping a coin

When flipping a coin, the sample - space is $\{H,T\}$. The event of getting heads or tails is the entire sample - space. So the probability is $\frac{2}{2}=1$.

• Event 5: landing on a blue or red space on a spinner with 1 blue space and 1 red space

The sample - space has 2 spaces (blue and red). The probability of landing on blue or red is $\frac{2}{2}=1$.

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