A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, the number is even, and B be the event, the number is red. Are A and B independent?

Answer

N/a

Explanation

When a die is thrown then
`S={1,2,3,4,5,6}`
Let `E=` event of getting an even number and
`B=` event that number is red.
`:.A={2,4,6},B={1,2,3}` and `AnnB={2}`
`impliesn(A)=3,n(B)=3,n(AnnB)=1`
Now, `P(A)=3/6=1/2,P(B)=3/6=1/2`
and `P(AnnB)=1/6`
and `P(A)xxP(B)=1/2xx1/2=1/4!=1/6=P(AnnB)`
`impliesP(AnnB)!=P(A)P(B)`
Therefoe A and B are not independent events.