Question

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

Answer 1

Answer:

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.

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Therefore,

$\implies \textsf{Probability of getting a red} = \sf \dfrac{3}{4}$

$\implies \textsf{Probability of getting a yellow} = \sf \dfrac{1}{4}$

Multiplication Rule for Independent Events

For independent events A and B:

• $\sf P(A\:and\:B)=P(A) \times P(B)$

Therefore,

$\begin{aligned}\implies \sf P(yellow\:and\:yellow) & = \sf P(yellow) \times P(yellow)\\\\ & = \sf \dfrac{1}{4} \times \dfrac{1}{4}\\\\ & = \sf \dfrac{1}{16}\end{aligned}$

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.

Answer 2

Answer:

I disagree.

Step-by-step 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.