首页
登录
职称英语
Let’s be a set of outcomes and let A and B be events with outcomes in S.Let-B de
Let’s be a set of outcomes and let A and B be events with outcomes in S.Let-B de
游客
2024-01-13
14
管理
问题
Let’s be a set of outcomes and let A and B be events with outcomes in S.Let-B denote the set of all outcomes in S that are not in B and let P(A)denote the probability that event A occurs.What is the value of P(A)?
(1) P(A ∪ B)=0.7
(2) P(A ∪ -B)=0.9
选项
A、Statement(1) ALONE is sufficient,but statement (2) alone is not sufficient.
B、Statement(2) ALONE is sufficient,but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient,but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements(1) and(2) TOGETHER are NOT sufficient.
答案
C
解析
The general addition rule for sets applied to probability gives the basic probability equation
P(A∪B) = P(A) + P(B) -P(A∩ B).
(1) Given that P(A ∪ B) = 0.7, it is not possible to determine the value of P(A) because nothing is known about the relation of event A to event B. For example, if every outcome in event B is an outcome in event A, then A ∪ B = A and we have P{A ∪ B) = P(A) = 0.7. However, if events A and B are mutually exclusive (i.e., P(A ∩ B) = 0) and P{B} = 0.2, then the basic probability equation above becomes 0.7 = P(A) + 0.2 - 0, and we have P{A} = 0.5; NOT sufficient.
(2) Given that P(A ∪ ~B) = 0.9, it is not possible to determine the value of P{A} because nothing is known about the relation of event A to event ~B. For example, as indicated in the first figure below, if every outcome in event ~B is an outcome in event A, then A ∪ ~B = A and we have P(A ∪ ~B) = P(A) = 0.9. However, as indicated in the second figure below, if events A and ~B are mutually exclusive (i.e., P(A ∩ ~B) = 0) and P(~B) = 0.2, then the basic probability equation above, with ~B in place of 5, becomes 0.9 = P{A} + 0.2 - 0, and we have P(A) = 0.7; NOT sufficient.
Given (1) and (2), if we can express events as a union or intersection of events A ∪ B and A ∪ ~B, then the basic probability equation above can be used to determine the value of P{A}.The figure below shows Venn diagram representations of events A ∪ B and A ∪ ~B by the shading of appropriate regions.
Inspection of the figure shows that the only portion shaded in both Venn diagrams is the region representing event A. Thus, A is equal to the intersection of A ∪ B and A ∪ ~B, and hence we can apply the basic probability equation with event A ∪ B in place of event A and event A ∪ ~B in place of event B. That is, we can apply the equation
P(C∪D) = P{C} + P(D) -P(C∩D)
with C = A ∪ B and D = A ∪ ~B. We first note that P(C) = 0.7 from (1), P(D) = 0.9 from (2), and P(C ∩D) = P(A). As for P(C ∪ D), inspection of the figure above shows that C ∪ D encompasses all possible outcomes, and thus P(C ∪ D) = 1. Therefore, the equation above involving events C and D becomes 1 = 0.7 + 0.9 - P(A), and hence P(A) = 0.6.
The correct answer is C;
both statements together are sufficient.
转载请注明原文地址:https://tihaiku.com/zcyy/3360065.html
相关试题推荐
Itwasconsideredimpolitebymanytodiscussbusinessonsocial______.A、events
Staffhavebeenholdinganumberof_________toraisemoneyforcharity.A、events
Let’sbeasetofoutcomesandletAandBbeeventswithoutcomesinS.Let-Bde
WhatisthegreatestprobabilitythateventsRandWwillbothoccur?(1)Thepr
ConsideraprobabilityexperimentwitheventsM,N,andLforwhichP(M)=0.25,
ConsideranexperimentwitheventsAandBTheprobabilityofeventAis0.63,a
ConsideranexperimentwitheventsAandB.TheprobabilityofeventAis0.63,
Inaprobabilityexperiment,GandHareindependentevents.Theprobabilitytha
Inaprobabilityexperiment,GandHareindependentevents.Theprobabilitytha
QuantityA:TheprobabilitythateventsRandWbothoccuris0.48QuantityB:t
随机试题
Thenaturalenvironmenthas,ofcourse,alwaysconditionedtechnology.Forex
Whattimewastheman’sappointment?[br][originaltext]M:Hello,Ihaveanapp
[originaltext]M:Ms.Lincoln,I’myourtenant,Joe.Ican’tgetconnectedonlin
关于儿童鼻窦炎,下述正确的是A.儿童鼻窦炎一般症状较轻 B.儿童较为严重鼻窦炎
夹套管安装就位后,应进行内、外管的吹扫工作。内管一般采用的吹扫介质为()。A:
以下不属于客户关系管理对理财业务发展的意义的是()。A.为理财师提供客户
患者,女性,25岁,低热、乏力、盗汗2周。近日体重下降明显,伴呼吸困难、胸痛,故
共用题干 AmericanWedding“Ido.”ToAmerican
初产妇,李某,孕期规律产检,今孕39周,规律宫缩10小时,宫口开大2cm,胎膜已
共用题干 某机械制造公司准备在其零部件部门安装一套最先进的计算机系统。这套系统
最新回复
(
0
)