1.

Cards with number 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has (i) an even number (ii) a square number

Answer» Total number of out comes with number 2 to 101, n(s)=100
(i) Let `E_(1)` =Event of selecting a card which is even number ={(2,4,6…10)} `["in an AP",l=a+(n-2)d, here l=100, a=2 and d=2 Rightarrow 100=2+(n-1)2 Rightarrow (n-1)=49 Rightarrow n=50]`
`therefore n(E_(1))=50`
`therefore "Required probability"= (n(E_(1))/(n(S))=(50)/(100)=(1)/(2))`
(ii) Let `E_(2)`=Event of selecting a card which is a square number
{(4,16,25,36,49,64,81,100)}
`{(2)^(2),(3)^(2),(4)^(2),(5)^(2),(6)^(2),(7)^(2),(8)^(2),(9)^(2),(10)^(2)}`
`therefore n(E_(2))=9`
Hence required probability=`(n(E_(2)))/(n(S))=(9)/(100)`


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