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 all will be blue?
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 all will be blue?
Total number of marbles $=10+20+30=60$
Number of ways of drawing $5$ marbles from $60$ marbles $=^{60} C_{5}$
All the drawn marbles will be blue if we draw $5$ marbles out of $20$ blue marbles.
$5$ blue marbles can be drawn from $20$ blue marbles in $^{20} C_{5}$ ways.
$\therefore$ Probability that all marbles will be blue $\frac{{^{20}{C_5}}}{{^{60}{C_5}}}$
Similar Questions
A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is
A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is
A box contains coupons labelled $1,2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x _3 < x _4 < x _5 ?$
A box contains coupons labelled $1,2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x _3 < x _4 < x _5 ?$
- [KVPY 2013]
If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are
If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are
In a collection of tentickets, there are two winning tickets. From this collection, five tickets are drawn at random Let $p_1$ and $p_2$ be the probabilities of obtaining one and two winning tickets, respectively. Then $p_1+p_2$ lies in the interval
In a collection of tentickets, there are two winning tickets. From this collection, five tickets are drawn at random Let $p_1$ and $p_2$ be the probabilities of obtaining one and two winning tickets, respectively. Then $p_1+p_2$ lies in the interval
- [KVPY 2021]
The probability of hitting a target by three marks men is $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu$ then $\lambda + \mu$ is equal to :-
The probability of hitting a target by three marks men is $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu$ then $\lambda + \mu$ is equal to :-