Question

Ari said there are three possible outcomes when you spin this spinner twice: two reds, a yellow and a red, or two yellows.

So, the probability of getting two yellows is 1/3

Do you agree or disagree? Explain your thinking.

Answer 1

I disagree.

Explanation:

The reasoning may be wrong but I believe it is disagree.

I am going to keep it simple.

On the spinner there are 4 options, 3 for red and 1 for yellow.

Therefore, we have a 1/4 chance to get a yellow once.

If we get a yellow again, it is another. 1/4 chance.

1/4 x 1/4 is 1/16, considerably smaller than 1/3.

Answer 2

From inspection of the diagram, we can see that the spinner is divided into 4 equal parts, where 3 parts are red and 1 part is yellow.

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

Therefore,

`\implies \textsf{Probability of getting a red} = \sf (3)/(4)`

`\implies \textsf{Probability of getting a yellow} = \sf (1)/(4)`

Multiplication Rule for Independent Events

For independent events A and B:

• 
  `\sf P(A\:and\:B)=P(A) * P(B)`

Therefore,

`\begin{aligned}\implies \sf P(yellow\:and\:yellow) & = \sf P(yellow) * P(yellow)\\\\ & = \sf (1)/(4) * (1)/(4)\\\\ & = \sf (1)/(16)\end{aligned}`

Conclusion

Ari is incorrect. The spinner is divided into 4 parts, where only one part is yellow. Therefore, the probability of spinning a yellow is 1/4. As the events are independent, the Multiplication Rule should be used to calculate the probability of spinning 2 yellows. So the probability of spinning 2 yellows is 1/4 x 1/4 = 1/16.