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Q.

Find the chance of throwing at least one ace in a single throw with two dice. ____.

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Detailed Solution

As we know that sample space in a single dice {1,2,3,4,5,6) = 6
So, total number of outcomes in two dice = 62
total number of outcomes in two dice =36
Now, we make sample space
(1,1)(2,1)(3,1)(4,1)(5,1)(6,1)
(1,2)(2,2)(3,2)(4,2)(5,2)(6,2)
(1,3)(2,3)(4,3)(4,3)(5,3)(6,3)
(1,4)(2,4)(3,4)(4,4)(5,4)(6,4)
(1,5)(2,5)(3,5)(4,5)(5,5)(6,5)
(1,6)(2,6)(3,6)(4,6)(5,6)(6,6)

Here {(1,2),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(3,1),(4,1),(5,1),(6,1)}at least one ace.
And rest have no ace in dice = 25
So, at least one ace = 11
Now, by using the formula of probability,
We know that the probability of an event E is given by =

\frac{Number of favourable outcomes}{Total number of outcomes}

Here, favourable outcomes = 11
and total number of outcome = 36
Then, P(at least one ace in a single throw) =

\frac{11}{36}

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