# Chapter 7: Chapter 7

Problem 6

Determine whether the events \(A\) and \(B\) are independent. $$ P(A)=.6, P(B)=.8, P(A \cap B)=.2 $$

Problem 6

Let \(S=\\{a, b, c, d, e, f\\}\) be a sample space of an experiment and let \(E=\\{a, b\\}, F=\\{a, d, f\\}\), and \(G=\) \(\\{b, c, e\\}\) be events of this experiment. Are the events \(E \cup F\) and \(E \cap F^{c}\) mutually exclusive?

Problem 6

Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. A pair is not drawn.

Problem 6

A pair of dice is rolled, and the number that appears uppermost on each die is observed.refer to this experiment and find the probability of the given event. The sum of the numbers is at least \(4 .\)

Problem 6

List the simple events associated with each experiment. Data concerning durable goods orders are obtained each month by an economist. A record is kept for a 1 -yr period of any increase \((i)\), decrease \((d)\), or unchanged movement \((u)\) in the number of durable goods orders for each month as compared with the number of such orders in the same month of the previous year.

Problem 7

List the simple events associated with each experiment. Blood tests are given as a part of the admission procedure at the Monterey Garden Community Hospital. The blood type of each patient (A, B, AB, or O) and the presence or absence of the \(\mathrm{Rh}\) factor in each patient's blood \(\left(\mathrm{Rh}^{+}\right.\) or \(\left.\mathrm{Rh}^{-}\right)\) are recorded.

Problem 7

Let \(S=\\{1,2,3,4,5,6\\}, E=\\{2,4,6\\}\) \(\boldsymbol{F}=\\{1,3,5\\}\), and \(\boldsymbol{G}=\\{5,6\\}\). Find the event \(E \cup F \cup G\).

Problem 7

Determine whether the events \(A\) and \(B\) are independent. $$ P(A)=.5, P(B)=.7, P(A \cup B)=.85 $$

Problem 7

Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. Two black cards are drawn.

Problem 8

Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. Two cards of the same suit are drawn.