sarah spins the spinner shown below. the likelihood that sarah will spin blue is 25%. the likelihood that…

sarah spins the spinner shown below. the likelihood that sarah will spin blue is 25%. the likelihood that sarah will spin green is 0.5. the likelihood that sarah will spin orange is $\frac{1}{4}$. select all the statements that are true. sarah is certain that the spinner will end on blue, orange, or green. it is as equally likely as not for sarah to spin orange as to spin blue. it is impossible for sarah to spin and get yellow. sarah is less likely to spin green than blue. it is more likely that sarah will spin orange than blue. it is impossible that sarah will spin blue. sarah is certain to spin orange.

sarah spins the spinner shown below. the likelihood that sarah will spin blue is 25%. the likelihood that sarah will spin green is 0.5. the likelihood that sarah will spin orange is $\frac{1}{4}$. select all the statements that are true. sarah is certain that the spinner will end on blue, orange, or green. it is as equally likely as not for sarah to spin orange as to spin blue. it is impossible for sarah to spin and get yellow. sarah is less likely to spin green than blue. it is more likely that sarah will spin orange than blue. it is impossible that sarah will spin blue. sarah is certain to spin orange.

Answer

Explanation:

Step1: Convert probabilities to common - form

The probability of spinning Blue is $P(B)=25% = 0.25$, the probability of spinning Green is $P(G)=0.5$, and the probability of spinning Orange is $P(O)=\frac{1}{4}=0.25$. The sum of these probabilities $P(B)+P(G)+P(O)=0.25 + 0.5+0.25 = 1$.

Step2: Analyze each statement

  • Statement 1: Since $P(B)+P(G)+P(O)=1$, Sarah is certain that the spinner will end on Blue, Orange, or Green. This statement is True.
  • Statement 2: The probability of spinning Orange is $P(O) = 0.25$, and the probability of not - spinning Orange is $1 - 0.25=0.75$. The probability of spinning Blue is $P(B)=0.25$. It is not equally likely as not for Sarah to spin Orange as to spin Blue. This statement is False.
  • Statement 3: Since the sum of probabilities of Blue, Green and Orange is 1, it is impossible for Sarah to spin and get Yellow. This statement is True.
  • Statement 4: $P(G)=0.5$ and $P(B)=0.25$, so Sarah is more likely to spin Green than Blue. This statement is False.
  • Statement 5: $P(O)=0.25$ and $P(B)=0.25$, so it is equally likely that Sarah will spin Orange and Blue. This statement is False.
  • Statement 6: $P(B)=0.25\neq0$, so it is not impossible that Sarah will spin Blue. This statement is False.
  • Statement 7: $P(O)=0.25\neq1$, so Sarah is not certain to spin Orange. This statement is False.

Answer:

Sarah is certain that the spinner will end on Blue, Orange, or Green.; It is impossible for Sarah to spin and get Yellow.