So I've been trying to solve this one which looks pretty straight forward, but I'm just not 100% sure about my solution. so any help is really appreciated.
Q: When 6 six-sided dice are rolled at the same time, whats the probability of getting at least 2 sixes?
I tried solving it by trying to find the probability of getting 0 and 1 six.
Probability of getting no sixes: (5/6)^6 = 0.3349
Probability of getting one six: 6*(1/6)(5/6)^5 = 0.4019
so the probability of getting at least two sixes is,
1 - (0.3349 + 0.4019) = 0.2632 ????
the probability of getting no sixes is pretty straight forward. however, getting one six was a bit tricky.. i considered a single instance of rolliing six dice where 1 dice has 1/6 of getting a six and the other 5 have 5/6 of not getting a six.. the outcome is, 6XXXXX.. and there are 6 different combinations of this.. so i multiplied it by six..
so what do you think.. is this correct or am I looking at it the wrong way? thanks for your help!