A coin is tossed three times. Let the events `A ,B` and `C` be defined as follows: `A=` first toss is head, `B=` second toss is head, and `C=` exactly two heads are tossed in a row. Check the independence of `A&B` `B&C` `C&A`

Explanation

Here, `A = {(HHH),(HHT),(HTH),(HT T)}`

`B = {(HHH),(HHT),(THH),(THT)}`

`C = {(HHT),(THH)}`

We can clearly see that `A` and `B` are completely independent.

Also, `B` and `C` are independent as in `C` head, is at the second toss.

So, it will not have any impact on `B`.

Now, there are elements in `A` where, two consecutive head are not present.

It means, `A` and `C` are dependent events.