statistics doubt.please help

[anushey]

okay so I was going throught the past papers and found a question that I was unable to solve.please if any one knows how to solve it please do tell me.
It is question 6 part c of Oct?nov 2012 variant 63

(c) Helen has some black tiles, some white tiles and some grey tiles. She places a single row of
8 tiles above her washbasin. Each tile she places is equally likely to be black, white or grey.
Find the probability that there are no tiles of the same colour next to each other.
please help me..



Also I want to know that in physics I have seen that marking schemes write answer to 2 significant figures.So should we write our anwers to 2 or 3 s.f?

 

[salvatore]

This is quite a tricky one..

The probability of placing each one of the coloured tile (Let's take an example of black) is 1/3.. right? The second tile must not be black, therefore: P(Not black) = 1 - 1/3 = 2/3.
The first tile could be any one of the three tiles, so the probability is 1 (Just for the first tile). The next seven tiles have the probability of 2/3.

Hence, the total probability becomes.. 1 * (2/3)^7 => 0.0585

Hope that helped

 

[anushey]

This is quite a tricky one..

The probability of placing each one of the coloured tile (Let's take an example of black) is 1/3.. right? The second tile must not be black, therefore: P(Not black) = 1 - 1/3 = 2/3.
The first tile could be any one of the three tiles, so the probability is 1 (Just for the first tile). The next seven tiles have the probability of 2/3.

Hence, the total probability becomes.. 1 * (2/3)^7 => 0.0585

Hope that helped

thankyou so much.!

 

[salvatore]

thankyou so much.!

You're welcome