Probability Set 4

Given then is equal to

A natural number is selected from 1 to 1000 at random, then the probability that a particular non-zero digit appears at most once, is

Let be three mutually independent events. Consider the two statements and are independent, are independent, then

A biased die is tossed and the respective probabilities for various faces to turn up are
Face              :    1       2         3        4        5        6

Probability :  0.1   0.24   0.19  0.18  0.15  0.14

If an even face has turned up, then the probability that it is face 2 or face 4, is

A bag contains 2 white and 3 black bails and another bag contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability for the ball chosen be white, is

Probability and then is equal to

speaks truth in 60% and in 50% of the cases. The probability that they contradict each other narrating the same incident is

Twelve tickets are numbered from 1 to 12. One ticket is drawn at random, then the probability of the number to be divisible by 2 or 3, is

and appeared for an interview for two posts. The probability of selection is and that of selection is The probability that only one of them is selected, is

If and are mutually exclusive events with ,then is equal to (Here, is the complement of the event )