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 $1 - \frac{{^{30}{C_5}}}{{^{60}{C_5}}}$
Similar Questions
Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is
Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is
A bag contains $6$ red, $5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red, is
A bag contains $6$ red, $5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red, is
From a pack of playing cards three cards are drawn simultaneously. The probability that these are one king, one queen and one jack is
From a pack of playing cards three cards are drawn simultaneously. The probability that these are one king, one queen and one jack is
Twenty tickets are marked the numbers $1, 2, ..... 20.$ If three tickets be drawn at random, then what is the probability that those marked $7$ and $11$ are among them
Twenty tickets are marked the numbers $1, 2, ..... 20.$ If three tickets be drawn at random, then what is the probability that those marked $7$ and $11$ are among them
If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks, then his chance of winning prize are
If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks, then his chance of winning prize are