Question

A bucket contains 8red,3 blue and 5 green marbles . If 4 marbles are drawn at random , what is the probabaility that 2 are and 2 are blue ? A. `(11)/(16)` B. `(3)/(16)` C. `(11)/(72)` D. `(3)/(65)` Select the correct answer from above options

Answer 1

Correct Answer - D Total number of marbles `=8+3+5=16` n(s) = Exhaustive number of cases `=` number of ways of drawing 4 marbles out of 16 `=""^(16)C_(4)=(16xx15xx14xx1 3)/(1xx2xx3xx4)=1820` `n( E)=` Number of cases when 2 marbles are red and 2are blue `=""^(8)C_(2)xx""^(3)C_(2)=(8xx7)/(1xx2)xx(3xx2)/(1xx2)=84` `implies `Required probability `=(10)/(120)=(1)/(12)`