3. (6 points) A target on a test firing range consists of a bull\'s-eye with two

Question

3. (6 points) A target on a test firing range consists of a bull's-eye with two concentric rings around it. A projectile is fired at the target. The probability that it hits the bull's-eye is 0.10, the probability that it hits the inner ring is 0.25, and the probability that it hits the outer ring is 0.45. a. What is the probability that the projectile hits the target? b. What is the probability that it misses the target? 4. (6 points) In a certain type of automobile engine, the cylinder head is fastened to the block by 10 bolts, each of which should be torqued to 60 N m. Assume that the torques of the bolts are independent. If each bolt is torqued correctly with probability 0.99, what is the probability that all the bolts on the cylinder head are torqued correctly?

Explanation / Answer

3)a)P(hits the target)=P(hits the bulls-eye)+P(hits the inner ring)+P(hits the outer ring)=0.1+0.25+0.45=0.80

b)P(it misses the target)=1-P(hits the target)=1-0.80=0.20

4)

P(all 10 bolts are torques correctly)=(0.99)10 =0.904382

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