Class 11 Math Algebra Probability

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?

(a) you both enter the same sections?

(b) you both enter the different sections?

Solution: My friend and I are among the $100$ students

Total number of ways of selecting $2$ students out of 100 students $=_{100}C_{2}$

(a) The two of us will enter the same section if both of us are among $40$ students or among $60$ students

$∴$ Number of ways in which both of us enter the same section = $_{40}C_{2}+_{60}C_{2}$

$∴$ Probability that both of us enter the same section

$=_{100}C_{2}_{40}C_{2}+_{60}C_{2} =99×100(39×40)+(59×60) =3317 $

(b) $P$ (we enter different sections)

$=1−$ $P$ (we enter the same section)

$=1−3317 =3316 $

Total number of ways of selecting $2$ students out of 100 students $=_{100}C_{2}$

(a) The two of us will enter the same section if both of us are among $40$ students or among $60$ students

$∴$ Number of ways in which both of us enter the same section = $_{40}C_{2}+_{60}C_{2}$

$∴$ Probability that both of us enter the same section

$=_{100}C_{2}_{40}C_{2}+_{60}C_{2} =99×100(39×40)+(59×60) =3317 $

(b) $P$ (we enter different sections)

$=1−$ $P$ (we enter the same section)

$=1−3317 =3316 $

Similar topics

determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

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