SOLUTION: You roll a single die 10 times: a. probability that at least one resut will be divisible by three. b. probability of getting exactly 2 sixes. Thank you in advance

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Question 320800: You roll a single die 10 times:
a. probability that at least one resut will be divisible by three.
b. probability of getting exactly 2 sixes.
Thank you in advance
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

In order for the result of rolling one die to be divisible by 3, the result of rolling the die must be either a 3 or a 6. Since there are six possible results and only two of them are considered a success, the probability of success on any one trial is

The probability of successes in trials where is the probability of success on any given trial is given by:

Where is the number of combinations of things taken at a time and is calculated by

The probability of at least successes in trials is equal to 1 minus the probability of at most successes in trials, or:

So for part a) you need:

Or in the common vernacular, highly likely.

For part b) you need:

And you can do your own arithmetic.

John