Question

identifying events with probability of 1
which of the following events has a probability of 1? choose three correct answers.
choosing a red
marble from a bag
containing red and
green marbles
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
drawing a peanut
from a bag of trail
mix with 4 types of
nuts
drawing a red card
from a stack of 20
red cards

Explanation:

Step1: Recall probability formula

Probability of an event \(E\) is \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). An event with probability \(1\) is a certain event (all outcomes are favorable).

Step2: Analyze "getting a heads or a tails when flipping a coin"

When flipping a coin, the sample space \(S = \{H,T\}\). The event \(E=\{H,T\}\). Using the formula \(P(E)=\frac{n(E)}{n(S)}\), where \(n(E) = 2\) (number of heads or tails) and \(n(S)=2\) (total coin - flip outcomes). So \(P(E)=\frac{2}{2}=1\).

Step3: Analyze no - information - about - spinner - details (assuming standard interpretation for "landing on a blue or red space on a spinner with 1 blue space and 1 red space")

The sample space \(S=\{\text{blue},\text{red}\}\). The event \(E = \{\text{blue},\text{red}\}\). Using the formula \(P(E)=\frac{n(E)}{n(S)}\), with \(n(E) = 2\) (blue or red) and \(n(S)=2\) (total spinner spaces). So \(P(E)=\frac{2}{2}=1\).

Step4: Note that for "drawing a peanut from a bag of trail mix with 4 types of nuts", if there are other nuts (say \(n\geq1\) other types), \(P=\frac{1}{1 + n}<1\). For "choosing a red marble from a bag containing red and green marbles", if there are green marbles (\(n_{green}\geq1\)), \(P=\frac{n_{red}}{n_{red}+n_{green}}<1\). For "drawing a red card from a stack of 20 red cards", it's a certain event (\(P = 1\), but if the stack has non - red cards, \(P<1\). Assuming standard problems (coin and spinner with two non - overlapping, all - inclusive color/side cases)

Answer:

"getting a heads or a tails when flipping a coin" and "landing on a blue or red space on a spinner with 1 blue space and 1 red space" (assuming standard all - inclusive, non - overlapping outcome interpretations for coin and spinner)