If 81 percent o f all vehicles at a certain emissions inspection pass the inspec

Question

If 81 percent o f all vehicles at a certain emissions inspection pass the inspection. Assuming that successive vehicles pass or fail independently of one another. Calculate the following probabilities: 23) All of the next five vehicl es inspected Exactly three of the next five vehicles inspected pass. 25) pass. a. 0.3547 b. 0.3527 c. 0.3507 0.3487 e. 0.4287 a. 0.1919 b. 0.1879 c. 0.1899 d. 0.1889 e. 0.1869 24) At least one of the next five vehicles inspected fail. Given that at least one of the next five vehicles inspected fail, what is the probability that exactly three of the next five vehicles inspected fail. 26) a. 0.6513 b. 0.6473 c. 0.6493 d. 0.6483 e. 0.6463 a. 0.2546 b. 0.2946 c. 0.3146 d. 0.3346 e. 0.3546

Explanation / Answer

Probability of vehicle passing = 0.81

23) P(next 5 vehicles passing) = 0.815 = 0.3487 (option d)

24) P(at least one of the next five vehicles fail) = 1 - 0.3487

= 0.6513 (option a)

25) Exactly three of the next five vehicles pass = 5C3 x 0.813 x 0.192

= 0.1919 (option a)

26) P(3 vehicles pass | at least one fail) = P(3 vehicles pass) / P(at least one fail)

= 5C2x0.812x0.193 / 0.6513

= 0.1919/0.6513

= 0.2946 (option b)

*(in the question, its given that 3 fail, but the available options are for 3 pass)

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