Question

Alice spins the spinner 3 times. What is the probability that she spins an A, then a B, and then a C?
http://static.k12.com/calms_media/media/332000_332500/332448/2/580a1a69ea83d3dd36df179e9d8ab7a5003d26d9/MS_ALG_A2_04_quiz_Q2_question.gif
A. 1/3


B. 1/9


C. 1/27


D. 1/12

Answer 1

@iGreen

Answer 2

@sonic400539
Very smart way of tagging people one at a time without leaving a trace!

Anyway, what is the probability of landing on A for the first spin?

Answer 3

Lol^

Answer 4

1/3

Answer 5

The probability of spinning A, B, or C are the same, so when we find one, we can multiply it by itself 2 times.

Answer 6

Yep, you got it.

Answer 7

Now multiply it by itself 2 times.

Answer 8

xD Yeah, I always clear them so I don't look desperate.

Answer 9

Good, what is the probability of landing on B in a subsequent spin?

Answer 10

2/3?

Answer 11

B is still one third of the whole circle, so there is not a better probability than A, do you agree?

Answer 12

Yes, I agree. It makes sense.

Answer 13

What about C, again in a subsequent spin?

Answer 14

1/3

Answer 15

All have an equal chance, correct?

Answer 16

Yes, each one has equal chance.
Now, the experiment of getting A, then B, then C is called a multi-step experiment. The probability is the product of the three individual probabilities IF the steps are independent of each other.

Answer 17

Here, independence means that the result of one spin does NOT affect the result of subsequent spins, which is the case here, so the multiplication rule mentioned above applies.

Answer 18

@sonic400539
ok so far?

Answer 19

I'm following it. (So far.)

Answer 20

So how would you find the answer to the problem?
If you have doubts, reread what I just posted to make sure you understand it. It is the key to your answering ALL similar problems.

Answer 21

I believe that it is B because 1/3 is A, B, and C and when added you have a total probability of 1/9.

Answer 22

Wait, the answer is C. 1/27. The chances are correct. Thanks for the help! Question: Closed

Answer 23

Exactly: Good work!
\(\color{blue}{\Large\checkmark}{Way~to~go!}\)