Question

You are dealt two cards successively (without replacement) from a shuffles deck of 52 playing cards. Find the probability that the first card is king and the second card is queen. 7. An IRS auditor randomly selects 3 tax returns from 58 tax returns of which 8 contain errors. What is the probability that she selects none of those containing errors? 8. 9. A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected will be defective? A study conducted at a college shows that 54% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 10 A sample of 4 different calculators is randomly selected from a group containing 17 that are defective and 36 that have no defects. What is the probability that at least one of the calculators is defective? 11. 12. A single card is drawn from a deck. Find the probability that it is a king or a club.

Answer 1

7:

Out of 52 cards, 4 are king and 4 are queen. After selecting first king, the number of cards remaining is 51 out of which 4 are queen. So the required probability is

P(first king, then queen) = (4/52) * (4/51) = 0.0060

Answer: 0.0060

8:

Number of ways of selecting 3 returns out of 58 is

$C(58,3)$

Out of 58 returns, 58-8 = 50 contains no error. So number of ways of selecting 3 returns out of 50 is

$C(50,3)$

So the probability of selecting 3 returns with no error is

$\frac{C(50,3)}{C(58,3)}=0.6352$

Answer: 0.6352