Use the following problem to answer questions 4 6 A computer stores receives a b

Question

Use the following problem to answer questions 4 6 A computer stores receives a box of a certain video game. The box contains 35 games of which 4 are defective. A quality-control inspector randomly chooses 6 games from the box. 4. What is the probability that exactly 2 are defective? a. 0.0111 b. 0.0075 c. 0.1667 d. 0.8333 e. 0.1163 5. What is the probability that 0 are defective? a. 0.05410 b. 0.45361 c. 0.15473 d. 0.00029 e. 0.9244:5 6. What is the probability that at most 3 are defective? a. 0.9997 b. 0.6102 c. 0.5464

Explanation / Answer

4) Probability that exactly 2 are defective means four are not defective and 2 are defective

undefective video games = 35 - 4 = 31

defective video games = 4

Probability (exactly 2 defective) = 31C4(selecting 4 good ones from 31) * 4C2 (selecting two faulty ones from total 4)/35C6 (selecting 6 from total 35 games) = 0.1163

Hence the correct answer is Option E

5)

Probability that 0 are defective = 31C6 (choosing all 6 from good lot) /35C6 (choosing any 6 from total lot) = 0.4536

Correct answer is Option B

6)

Probability at most 3 defective = P(0 defective) + P(1 defective) + P(2 defective) + P(3 defective)

=> 1 - P(all are defective, since there are four defective only)

=> 1 - 31C2 * 4C4/35C6

=> 1 - 0.000286

=> 0.9997

Correct answer is Option A

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