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 Select the correct answer from above options

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.