Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that (a) you both enter the same section? (b) you both enter the different sections?

Answer

N/a

Explanation

Let `A=` section of 40 students
`B=` section of 60 students
No. of ways of dividing 100 students into two sections of 40 and 60 students `=.^(100)C_(40)`
(a) No. of ways that both enter the section A
`=.^(2)C_(2)xx.^(98)C_(58)=.^(98)C_(58)`
No.of ways that both enter the same section
`=.^(98)C_(38)+.^(98)C_(58)`
Probability that both enter the same section
`=(.^(98)C_(38)+.^(98)C_(58))/(.^(100)C_(40))`
`=(|__40|__60)/(|__100)[(|__98)/(|__38|__60)+(|__98)/(|__40|__58)]`
`=(|__98)/(|__100)[(|__40)/(|__38)+(|__60)/(|__58)]`
`=(40xx39+60xx59)/(100xx99)=5100/9900=17/33`
(b) Probability that both enter the different section
`=1-` probability that both enter the same section
`=1-17/33=16/33`