Twelve students sit in a classroom, with seven students in the first row and the other five students in the second row. Three students are chosen randomly from the class.

The probability that exactly two of the three students chosen are in the first row is

1. \(\dfrac{7}{44}\)
2. \(\dfrac{21}{44}\)
3. \(\dfrac{5}{22}\)
4. \(\dfrac{245}{576}\)

A bag contains three red pens and `x` black pens. Two pens are randomly drawn from the bag without replacement. The probability of drawing a pen of each colour is equal to

1. `\frac{6 x}{(2+x)(3+x)}`
2. `\frac{3 x}{(2+x)(3+x)}`
3. `\frac{x}{2+x}`
4. `\frac{3+x}{(2+x)(3+x)}`
5. `\frac{3+x}{5+2 x}`

A box contains  `n`  marbles that are identical in every way except colour, of which  `k`  marbles are coloured red and the remainder of the marbles are coloured green. Two marbles are drawn randomly from the box.

If the first marble is not replaced into the box before the second marble is drawn, then the probability that the two marbles drawn are the same colour is

1. `(k^2 + (n-k)^2)/n^2`
2. `(k^2 + (n-k-1)^2)/n^2`
3. `(2k(n-k-1))/(n(n-1))`
4. `(k(k-1) + (n-k)(n-k-1))/(n(n-1))`
5. `\ ^n C_2 (k/n)^2 (1-k/n)^(n-2)`

A bag contains three white balls and seven yellow balls. Three balls are drawn, one at a time, from the bag, without replacement.

The probability that they are all yellow is

1. `3/500`
2. `27/1000`
3. `21/100`
4. `7/24`
5. `243/1000`

A box contains six red marbles and four blue marbles. Two marbles are drawn from the box, without replacement.

The probability that they are the same colour is

1. `1/2`
2. `28/45`
3. `7/15`
4. `3/5`
5. `1/3`

A bag contains five red marbles and four blue marbles. Two marbles are drawn from the bag, without replacement, and the results are recorded.

The probability that the marbles are different colours is

1. `20/81`
2. `5/18`
3. `4/9`
4. `40/81`
5. `5/9`