Two whole numbers are randomly selected and multiplied. Consider two events `E_1 and E_2` defined as `E_1` : Their product is divisible by 5 and `E_2` Unit's place in their product is 5 Which of the following statement(s) is/are correct?

Options

A. `E_(1)` is twice as likely to occur as `E_(2)`
B. `E_(1)and E_(2)` are disjoint
C. `P(E_(2)//E^(1))=1//4`
D. `P(E_(1)//E_(2))=1`

Answer

C, D

Explanation

`P(E_(1))=1-P("unit's plac in both is"1,2,3,4,6,7,8,9,)`
`P(E_(1)=0or5)=1-((4)/(5))^(2)=(9)/(25)`
`P(E_(2),5)=P(13579)-P(1379)`
` =1/4=4/25`
`(25-16)/(100)=(9)/(100)`
`(P(E_(2)))/(P(E_(1)))=9/100xx25/9=1/4`
`P(E_(1))=4P(E_(2))`
`P(E_(2)//E_(1))=(P(E_(2)nnE_(1)))/(P(E_(1)))=(P(E_(2)))/(P(E_(1)))=1/4`
`P(E_(1)//E_(2))=(P(E_(1)nnE_(2)))/(P(E_(2)))=(P(E_(2)))/(P(E_(2)))=1`