Please show all steps using the formula : p1 +p2 + pn = 1

Find the probability distribution of the value x. mean variance and standard derivation.

1. two dice are rolled . x is the sum of numbers on the top faces.

2. five cards are randomly selected from a standard deck.
x is the number of aces in the sample.

3. It is known that 20% of old cars cannot pass the emission test . Four old cars are selected randomly . x is the number of card in the sample that cannot pass the emission test.

4. The probability that a new car is damaged is 0.02. 400 cars are being inspected . what is the probability that the number of damaged cars in the sample is :
a. 0

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