You are tossing a coin, and rolling a dice. What is the probability that you get a head in toss or an odd number in die?

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Probability for tossing on heads$=0.5$ Probability of rolling on odd number on die (1 or 3 or 5)$= 0.5$ As per addition rule (A union B, A or B) that is $0.5 + 0.5 = 1$ that seems impossible. How could it be? You could very well get a tail and an even-numbered die. Is it a paradox?

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The addition rule only works for disjoint events (i.e. if they can't both happen). In general the rule is $$P(A\cup B)=P(A)+P(B)-P(A\cap B).$$ In this case $A$ and $B$ are independent, so you can use the rule for independent events $$P(A\cap B)=P(A)P(B);$$ using both these rules will allow you to work out what you want.