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 sections? (b) you both enter the different sections?
Out of total 100 students, two section of 40 and 60 students formed. I and my friend are among the 100 students.
Total number of ways selecting two students out of hundred students is 100 C 2 .
(i)
The number of ways in which both enter in the same section is 40 C 2 + 60 C 2 .
Assume, a be the event for both enter the same section.
Probability that both enter in the same section is,
P ( a ) = 40 C 2 + 60 C 2 100 C 2 = 40 ! 2 ! 38 ! + 60 ! 2 ! 58 ! 100 ! 2 ! 98 ! = ( 39 × 40 ) + ( 59 × 60 ) { 99 × 100 } = 17 33
Thus, probability is 17 33 .
(ii)
The probability that both enter in the different section is,
P ( different sections ) = 1 − P ( a ) = 1 − 17 33 = 16 33
Thus, required probability is 16 33 .
Out of total
Total number of ways selecting two students out of hundred students is
(i)
The number of ways in which both enter in the same section is
Assume, a be the event for both enter the same section.
Probability that both enter in the same section is,
Thus, probability is
(ii)
The probability that both enter in the different section is,
Thus, required probability is
