1 Two numbers are chosen at random from among the integers 1

1. Two numbers are chosen at random from among the integers 1 to N without replacement. (a) Find probability that the second number chosen is 1?

2. Of cars sold 45% have a small engine, 55% have a large engine. With a small engine, 10% fail emissions testing, while 15% of large engines fail testing. Record of failed emissions test is chosen at random.(b) What is the probability it is a car with a small engine?

3. Police records show in a city that the probability is .45 that a burglar will be caught and .30 that a burglar will be caught and convicted. (c) What is the probability that if caught a burglar will be convicted?

4. A carpenter determines that he will have a net profit of 4500$ if he gets a contract and a net loss of $100 if his bid fails. (d) If the probability of getting a contract is 0.3 calculate net profit?

Solution