91Ó°ÊÓ

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. Find the events \(F^{c}\) and \(E \cap G^{c}\).

List the simple events associated with each experiment. An opinion poll is conducted among a group of registered voters. Their political affiliationDemocrat \((D)\), Republican \((R)\), or Independent \((I)-\) and their sex-male \((m)\) or female \((f)-\) are recorded .

Let \(A\) and \(B\) be two events in a sample space \(S\) such that \(P(A)=.6\) and \(P(B \mid A)=.5 .\) Find \(P(A \cap B)\)

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. A double is thrown.

List the simple events associated with each experiment. As part of a quality-control procedure, eight circuit boards are checked, and the number of defective boards is recorded.

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. Find the events \(E^{c}\) and \(F^{c} \cap G\).

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 \(E\) and \(F\) mutually exclusive?

List the simple events associated with each experiment. In a survey conducted to determine whether movie attendance is increasing \((i)\), decreasing \((d)\), or holding steady \((s)\) among various sectors of the population, participants are classified as follows: Group \(1:\) Those aged \(10-19\) Group 2: Those aged 20-29 Group 3: Those aged \(30-39\) Group 4: Those aged 40-49 Group 5: Those aged 50 and older The response and age group of each participant are recorded.

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 drawn.

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. One die shows a 6 , and the other is a number less than 3 .