Determine the probability when two fair dice The sum is at most 5 or at least 10 The sum is prime or divisible by 6

Solution

De t er min e t h e p ro babi l i t y w h e n tw o f ai r d i ce T h e s u m i s a t m os t 5 or a t l e a s t 10 T h e s u m i s p r im e or d i v i s ib l e b y 6

Solution

\frac{19}{36}

Decimal

0.52777 \dots

Solution steps

The possible outcomes when two dice are rolled are

6 \cdot 6

Therefore, the number of possible outcomes:

6^{2}

Find the number of favorable outcomes of when 2 fair dice The sum is at most 5 or at least 10 The sum is prime or at least 10 The sum is prime or divisible by 6:

19

Probability

= \frac{number of favorable outcomes}{total number of outcomes}

= \frac{19}{6 ^{2}}

6^{2} = 36

= \frac{19}{36}

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