1cud u elaborate q2 ...the symbols r not clear
Q1 if n postiive integers are taken at random and multiplied together and pn is probablity that last digit of product is 2,4,6,8.Find pn and p4
Q2 2 integers r,s are drawn one at a time without relacememnt from set 1,2,3...n.If pk=P(r≤k l s≤k).Find 4p7 if n=25
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9 Answers
11)
all we requite is that atleast one of the n integers must be even n none of them must be divisivle by five
because only 2x5 will end in 0 rest all will give 2,4,6 or 8
prob integer is even =1/2
prob integer is not divisible by five and two=1-1/5-1/2+1/10=2/5
so probability = \sum_{r=1}^{n}{{n\choose r}\left(\frac{1}{2} \right)^r\left(\frac{2}{5}\right)^{n-r}}
=\left(\frac{1}{2}+\frac{2}{5} \right)^n - {n\choose 0}\left(\frac{2}{5}\right)^n
=\left(\frac{7}{10} \right)^n - {n\choose 0}\left(\frac{2}{5}\right)^n
This is wrong as cases become too complicated n selection not required
1i have taken that the set of numbers from which we r choosing is not limited...i.e. all natural numbers
1got the first one......
we first include all possible numbers....
we see that in no way numbers divisible by five...(as it will then end in 0 or 5)
all other numbers are permitted
we see that 4 out of every 5 numbers is not divisible by 5
so \left(\frac{4}{5}\right)^n
but in this we have included a case where all numbers end with either 1 or 3.....but atleast one even is required
so we have to subtract
\left(\frac{2}{5}\right)^n cases
as 2 out of every 5 number ends by 1 or 3
hence the ans
\left(\frac{4}{5}\right)^n-\left(\frac{2}{5}\right)^n
24whats not clear ??
its 4. p7 where pk=P(r≤k l s≤k)
** l denotes ""such that ""