The probability that a randomly chosen factor of $10^{19}$ is a multiple of $10^{15}$ is

A man is known to speak the truth on an average 4 out of 5 times. He throws a die and reports that it is a five. The probability that it is actually a five is

A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is

The probability that a randomly chosen positive divisor of $10 ^ {2023}$ is an integer multiple of $10 ^ {2001}$ is

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.8 is

In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2, 4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to

A fair die is rolled repeatedly. The probability that the cumulative sum is at least 17 in the third trial is