Question:
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:
Total Students = 100
a. Probability that both enter in the same section = (40C2 + 60C2)/100C2 (either in first group or in second group)
= {(40*39)/2 + (60*59)/2}/{(100*99)/2}
= {(40*39) + (60*59)}/{100*99}
= {(4*39) + (6*59)}/{10*99}
= (156 + 354)/990
= 510/990
= 51/99
= 0.5151
a. Probability that both enter in the different section = (40C1*60C1 + 60C1*40C1)/100C2
= (40*60 + 60*40)/(100*99/2)
= (4*6 + 6*4)/(99/2)
= {2*(24 + 24)}/99
= (2*48)/99
= 96/99
= 0.9697
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