首页
登录
职称英语
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 light
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 light
游客
2024-01-12
57
管理
问题
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?
Give your answer as a fraction.
选项
答案
153/190
解析
The desired probability corresponds to the fraction
the number of ways that 2 lightbulbs, both of which are not defective, can be chosen
the number of ways that 2 lightbulbs can be chosen
In order to calculate the desired probability, you need to calculate the values of the numerator and the denominator of this fraction.
In the box there are 20 lightbulbs, 18 of which are not defective. The numerator of the fraction is the number of ways that 2 lightbulbs can be chosen from the 18 that are not defective, also known as the number of combinations of 18 objects taken 2 at a time.
If you remember the combinations formula, you know that the number of combinations is
(which is denoted symbolically as
or
). Simplifying, you get
Similarly, the denominator of the fraction is the number of ways that 2 lightbulbs can be chosen from the 20 in the box, which is
. Therefore, the probability that neither of the lightbulbs selected will be defective is 153/190. The correct answer is 153/190(or any equivalent fraction).
Another approach is to look at the selection of the two lightbulbs separately. The problem states that lightbulbs are selected simultaneously. However, the timing of the selection only ensures that the same lightbulb is not chosen twice. This is equivalent to choosing one lightbulb first and then choosing a second lightbulb without replacing the first. The probability that the first lightbulb selected will not be defective is 18/20. If the first lightbulb selected is not defective, there will be 19 lightbulbs left to choose from, 17 of which are not defective. Thus, the probability that the second lightbulb selected will not be defective is 17/19. The probability that both lightbulbs selected will not be defective is the product of these two probabilities. Thus, the desired probability is
. The correct answer is 153/190(or any equivalent fraction).
转载请注明原文地址:https://tihaiku.com/zcyy/3355803.html
相关试题推荐
Ofthe20lightbulbsinabox,2aredefective.Aninspectorwillselect2light
Eachyear,themembersofabookclubselectnovelsandnonfictionbookstoread
Inaboxof10electricalparts,2aredefective.(a)Ifyouchooseonepartatr
Inaboxof10electricalparts,2aredefective.(a)Ifyouchooseonepartatr
Fromaboxof10lightbulbs,youaretoremove4.Howmanydifferentsetsof4l
Inaboxof10electricalparts,2aredefective.(a)Ifyouchooseonepartatr
Ifanintegerisrandomlyselectedfromallpositive2-digitintegers,whatist
Fromaboxof10lightbulbs,youaretoremove4.Howmanydifferentsetsof4l
Aboxcontains5orangedisks,4reddisks,and1bluedisk.Youaretoselectt
Supposeyouwanttoselecta3-personcommitteefromagroupof9students.How
随机试题
Thissummer,Texas’droughtofthecenturyisanuncomfortablereminderthat
A. B. C. D.
在信息系统试运行阶段,系统失效将对业务造成影响。针对该风险,如果采取“接受”的方
患病率的计算方法是A.(特定时间点某人群中某病的新旧病例数/观察人口)×k B
关于电击伤的叙述哪项不正确A.高频交流电危害性较低频交流电为大 B.交流电的危
产权比率等于负债总额除以()。A.资产总额 B.股东权益总额 C.利润
某债券面值为100元,票面利率为6%,每年付息一次,起息日是8月5日,交易日是1
自然人的民事权利能力始于出生终于死亡。( )
董某前往个体工商户邵某的“邵氏手机店”,打算购买一块手机锂电池。由于生意火爆,邵
关于钢结构高强度螺栓连接,下列说法正确的有()。A.高强度螺栓可以兼作安装
最新回复
(
0
)