Q.​Q.A random survey was conducted in a small towns about the soaps used by females of different age groups.
Find Probability that female chosen at random is from age groups.
i) a)(13-23)years & likes pears
b)above 35 years & likes medimix
c)(5-12) years & likes Dove.


NOTE:PLEASE DON'T PROVIDE LINKS...

Answer :

We know probability  P ( E ) = $\frac{Total number of desired events n (\hspace{0.17em}E\hspace{0.17em})}{Total number of events n (\hspace{0.17em}S\hspace{0.17em})}$
So,

Here Total number of females  =  53 + 30 + 10 + 7 + 21 + 49 + 35 + 42 + 50 + 33 + 25 + 20 + 20 + 25 + 35 =  455
So,
n ( S ) =  455

i ) Probability that female chosen at random is from age groups. ( 13 - 23 ) years & likes pears , So

n ( E ) =  49 
So,
Probability that female chosen at random is from age groups. ( 13 - 23 ) years & likes pears = $\frac{49}{455} = \frac{\mathbf{7}}{\mathbf{65}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathbf{ }\mathbf{)}$

ii ) Probability that female chosen at random is from age groups. above 35 years & likes medimix , So

n ( E ) = 25
So,
Probability that female chosen at random is from age groups. above 35 years & likes medimix  = $\frac{25}{455} = \frac{\mathbf{5}}{\mathbf{91}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathbf{ }\mathbf{)}$

iii ) Probability that female chosen at random is from age groups. ( 5 - 12  ) years & likes Dove, So

n ( E ) =  53
So,
Probability that female chosen at random is from age groups.( 5 - 12  ) years & likes Dove = $\frac{\mathbf{53}}{\mathbf{455}} \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathbf{ }\mathbf{)}$