Question

A coin is tossed thrice and all the eight outcomes are assumed equally likely. In which of the following cases are the following events `A` and `B` are independent? `A=` the first thrown results in head, `B=` the last thrown results in tail `A=` the number of heads is odd, `B=` the number of tails is odd `A=` the number of heads is two, `b=` the last throw results in head

Answer 1

(i) `A =` the first thrown results in head,
`B =` the last thrown results in tail.
These two events are independent as first and third toss will not have any imapct on each other.

(ii)`A =` the number of heads is odd,
`B =` the number of tails is odd.
As there are `3` tosses, it means either number of heads is odd or number of tails is odd.
But, both can not be odd.
So, these two events are dependent.

(iii)`A =` the number of heads is two,
`B =`the last throw results in head.
There can be a case when first two tosses are heads from event `A` and the last throw is head from event `B`.
Then, there can be three heads that is a conflict with event `A`.
So, these two events are dependent.