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The probablity of filliping a coin and getting 2 heads (HH) is:
(1/2)*(1/2)=1/4
Getting HT = (1/2)*(1/2)
Getting TH = (1/2)*(1/2)
Getting TT = HH = 1/4
So 50% of the time (1/4+1/4=1/2) you'll get the TH, HT combination and 25% of the time you'll get HH and 25% of the time you'll get TT.
Now just extending this to the problem from the initial post.
The probablity of getting 2 heads (HH) by rolling 2 times on this 5 sided dice is
(1/5)*(1/5)=(1/5)^2
The probablity of getting anything but heads (XXXXXX) and rolling 6 times is
(4/5)*(4/5)*(4/5)*(4/5)*(4/5)*(4/5)=(4/5)^6
Now the probablity of getting 2 out of 8 times of this 5 side dice is just
mutlitplying the above probabilities. (HHXXXXXX, where 'X' means anything but Heads)
=(1/5)^2 * (4/5)^6
I get the same answer as Myst.
(hopefully there aren't too many typos)
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