In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.

A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually six.

In a hockey match two teams A and B scored same number of goals upto the end of the games so as to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.

A man is known to speak the truth 2 times out of 3 times. He throws a fair die and reports that it is .4. Find the probability that it is actually a 4.

A man is known to speak the truth 4 times out of 5 times. He throws a fair die and reports that it is 2. Find the probability that it is actually a 2.

A man is known to speak the truth 3 out of 5 times. He throws a die and reported that it is a number greater than 4. Find the probability that it is actually a number greater than 4.