A box contains $10$ red marbles, $20$ blue marbles and $30$ green marbles. $5$ marbles are drawn from the box, what is the probability that atleast one will be green?
A box contains $10$ red marbles, $20$ blue marbles and $30$ green marbles. $5$ marbles are drawn from the box, what is the probability that atleast one will be green?
Total number of marbles $=10+20+30=60$
Number of ways of drawing $5$ marbles from $60$ marbles $=^{60} C_{5}$
Number of ways in which the drawn marbles is not green ${ = ^{(20 + 10)}}{C_5}{ = ^{30}}{C_5}$
$\therefore$ Probability that no marble is green $=\frac{^{30} C_{5}}{^{60} C_{5}}$
$\therefore$ Probability that at least one marble is green $1 - \frac{{^{30}{C_5}}}{{^{60}{C_5}}}$
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