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Probability and Statisics

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

b. 2

c. more than 2

Solution Preview

(1) The probability distribution is:

x = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

with the corresponding probabilities being

P(x) = 1/36, 1/18, 1/12, 1/9, 5/36, 1/6, 5/36, 1/9, 1/12, 1/18, 1/36

(a) Mean = sum of x * P(x)

= 2(1/36) + 3(1/18) + 4(1/12) + 5(1/9) + 6(5/36) + 7(1/6) + 8(5/36) + 9(1/9) + 10(1/12) + 11(1/18) + 12(1/36) = ...

Solution Summary

The expert examines probability and statistics in formulas. Neat, step-by-step solutions are provided.

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