A fair coin and an in biased die are tossed. Let A be the event head appears on the coin and B be the event 3 one the die. Check whether A and B are independent event or not.

Answer

N/a

Explanation

If a fair coin and an unbiased die is thrown then
`S={{:((H,1)","(H,2)","(H,3)","(H,4)","(H,5)","(H,6)),((T,1)","(T,2)","(T,3)","(T,4)","(T,5)","(T,6)):}}`
`implies n(S)=12`
Let `A=` event of getting head and
`B=` event of getting a number 3.
`:. A={(H,1),(H,2),(H,3),(H,4),(H,5),(H,6)}`
and `B={(H,3),(T,3)}`
`impliesAnnB={H,3}`
`impliesn(A)=6,n(B)=2,n(AnnB)=1`
Therefore `p(A)=6/12=1/2, P(B)=2/12=1/16`
and `P(AnnB)=1/12`
Now `P(A)xxP(B)=1/2xx1/2=1/12=P(AnnB)`
Therefore A and B are independent events.