For a loaded die, the probabilities of outcomes are given as under: `P(1)=P(2)=2/(10),P(3)=P(5)=P(6)=1/(10)a n dP(4)=3/(10)` The die is thrown two times. Let A and B be the events as defined below A=Getting same number each time, B=Getting a total score of 10 or more. Determine whether or not A and B are independent events.

Explanation

Die is thrown two times.

Here, A= Same number each time

and B= Total score is 10 or more

therefore` A={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}`
`
So, P(A)=[P(1,1)+P(2,2)+P(3,3)+P(4,4)+P(5,5)+P(6,6)]`
`
=[P(1) cdot P(1)+P(2) cdot P(2)+P(3) cdot P(3)+P(4) cdot P(4)+P(5) cdot P(5) +P(6) cdot P(6)]`
`
=[0.2 times 0.2+0.2 times 0.2+0.1 times 0.1+0.3 times 0.3+0.1 times 0.1+0.1 times 0.1] =0.20`

and `B={(4,6),(6,4),(5,5),(5,6),(6,5),(6,6)}`

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