Given
For a loaded die –
P (1) = P (2) = 0.2, P (3) = P (5) = P (6) = 0.1 and P (4) = 0.3
The die is thrown twice and
Therefore, for A,
For B,
B= EVENT OF TOTAL SCORE IS 10 OR MORE
B= {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
For the probability of intersection B i.e. both the events occur simultaneously,
Therefore,
P (A B) = P (5,5) + P (6,6)
P (A B) = P (5) × P (5) + P (6) ×P (6)
P (A B) = 0.1×0.1+ 0.1×0.1
P (A B) = 0.01+0.01
P (A B) = 0.02
Knowing that if two events are independent, then,
Therefore,
Hence, A and B are independent events.