A natural number x is chosen at random from the first 100 natural numbers. What is the probability that x² + x > 50?

A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  

Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?

For two events A and  B, P(A) = P(A|B) = 0.25 and P(BIA) = 0.5. Which of the following are correct?

I. A and B are independent.

II. P(A^c ∪ B^c) = 0.875

III. P(A^c ∩ B^c) = 0.375

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