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Question:Show that the Probability that the announcement of new train b/n Bangalore & Chennai in the rail budget is equal to 1?
Solution:Let E1 be the event of announcing new train b/n Bangalore & Chennai in the rail budget & E2 be the event of not announcing new train b/n Bangalore & Chennai in the rail budget.Then P(E1) is the probability of announcing new train b/n B & C,P(E2) is the probability of not announcing new train b/n B & C.Now we have to prove that P(E1)=1 => P(E2)=0.
For this case i...
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have considered the Railway budgets fm 2003-04 to 2013-14 total 10 railway budgets.
1)2003-04 RB:17311/17312 Chennai-Yesvatnpur-vasco Weekly.
12691/92 Bangalore -Chennai Weekly.
15227/28 Yesvantpur-Chennai-Muzaffarpur weekly.
2)2004-05 RB:17313/14 Hubli-Yesvantpur-Chennai weekly.
3)2005-06 RB:12027/28 Bangalore-Chennai Shatabdi Exp Exc tuesday.
4)2006-07 RB:12577/78 Bangalore-Chennai-Darbhanga Exp weekly.
12509/10 Bangalore-Chennai-Guwahati Exp fm bi to triweekly.
5)2007-08 RB:12291/92 Yesvantpur-Chennai Exp weekly.
12295/96 Bangalore-Chennai-Patna fm 2 days to 6 days/week.
6)2008-09 RB:15901/02 Yesvantpur-Perambur-Dibrugarh town Weekly.
7)2009-10 RB:None(Mini RB not full fledged one)
8)2010-11 RB:12295/96 Bangalore-Chennai-Patna fm 6 days to daily.
9)2011-12 RB:22601/02 Shirdi-Bangalore-Chennai Weekly.
22681/82 Mysore-Bangalore-Chennai Weekly.
10)2012-13:22625/26 Bangalore-Chennai AC Double Decker Exp Daily.
11)2013-14:22351/52 Yesvantpur-Chennai-Pataliputra Exp Weekly.
12551/52 Yesvantpur-Chennai-Kamakhya AC Exp weekly.
So out of the 10 RBs in the 9 RBs E1 has occured & E2 has occured only one time.Probability of an event happening =Number of ways it can happen/Total number of outcomes.Here there r two events E1 & E2.
Therefore P(E1)=9/10=0.9,P(E2)=1/10=0.1
If we igonore the RB 2009-10 which is not full fledged one then P(E1)=9/9=1 & P(E2)=0/9=0.
So the Probability that the announcement of new train b/n Bangalore & Chennai in the rail budget is equal to 1.Hence the statement.
Now in the RB 2014-15 excepted announcements for B & C:
Extension of Chennai-Santragachi AC exp to Bangalore or increase in the freq of Hubli-Chennai fm weekly to 4 days or increase in freq of Bangalore-Guwahati exp fm 3 days to 5 days or Yesvantpur-Chennai AC exp weekly.