1. ## A Probability problem

There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after
being defective. What is the probability that same musical sound would be produced 5 times
consecutively?

Please post the answer soon. I have doubt between 1/32 and 1/16

2. If the toy is now defective, it has only two sounds to pick.

Each time, the probability is 1/2 and since the question asks for 5 times, it simplies that you have:

$P(5\ times\ same\ sound) = \dfrac12 \times \dfrac12 \times\dfrac12 \times\dfrac12 \times\dfrac12= \left(\dfrac12\right)^5 = \dfrac{1}{32}$

EDIT: I forgot the second case, see below.

3. Ok thanks a lot. But i have a doubt here.
Lets take the two sounds to be named as 0 and 1
so that the probable patterns are

00000
00001
00010
.
.
.
.
11110
11111

There are 32 pattern here.
But patterns with same sound repeating five times is 00000,11111
i.e. 2

so isn't it 2/32=1/16??

i know my explanation is somewhere wrong.
But i can't get where i go wrong.
Is it my understanding of the question wrong?? Or this is not the method??

ex) Probability of getting same face in tossing a coin coin thrice is 2 out of 8 possibilities rite??

isn't it similar??

4. Oh, duh, you're right. I didn't consider this. I'm a little tired, sorry for that.

Let's say it like this.

When the toy is defective, there are two sounds possible, 0 and 1 (using what you used)

$P(5\ times\ same\ sound) = P(5\ times\ 0) + P(5\ times\ 1) = \left(\dfrac12\right)^5 + \left(\dfrac12\right)^5 = \dfrac{1}{16}$

5. No, considering the problem well, the answer is indeed 1/16.

You showed it yourself.

3rd link: Wrong (the person even concluded that the probability was 32!?)
5th link: Wrong (uh... again the same person!?)

1/16 is the right answer, let me assure you. You thought well

6. Thanks a lot

I had a huge doubt like how can be all the links wrong and i can be rite... Thanks a lot..

7. Originally Posted by sathishwizard
There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is the probability that same musical sound would be produced 5 times consecutively?
That problem statement is really poorly written.
I did not reply after I first read it for that reason.
If we take it to mean one particular tune then the answer is $\frac{1}{32}$.
If we take it to mean either of the remaining tunes then the answer is $\frac{1}{16}$.

But why even mention the original ten tunes?
It would make sense to ask “What is the probability that one particular tune of the original ten tunes, is played five consecutive after being disabled?”
That is an interesting question.