1. ## Probability Q Again..

The number showing on the upper faces when two fair six-sided dice are tossed is observed. Consider events A and B defined as:
A - the total score is at least 8
B - at least one die achieves a score of 2 or less

Find
1. P(B') (in 3 dec pl)
2. P(A or B) ( in 3 dec pl)

Thanks

2. 1) We have 36 possible cases and 12 favourable cases: (1,1), (1,2), (1,2), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6).
So $\displaystyle P(B)=\frac{12}{36}=\frac{1}{3}$.

2) $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.
For $P(A)$: we have 15 favourable cases, so $\displaystyle P(A)=\frac{15}{36}=\frac{5}{12}$
For $P(A\cap B)$ we have 2 favourable cases, so $P(A\cap B)=\displaystyle\frac{2}{36}=\frac{1}{18}$.
Then $P(A\cup B)=\displaystyle\frac{5}{12}+\frac{1}{3}-\frac{1}{18}$