A bag contains red, blue and green counters.

The number of red counters is \(x + 4\).

The number of blue counters is \(3x - 3\).

The number of green counters is \(3x + 4\).

A counter is taken from the bag at random. The probability that it is blue is \(\frac{6}{17}\).

A spinner can land on blue, purple, orange or red.

The table shows the probability of each colour.

A bag contains \(24\) chips. Some of them are blue and the rest are yellow.

Omar takes a chip at random from the bag, records its colour, and puts it back.

He then takes a second chip at random from the bag.

The probability that both chips are blue is \(\frac{ 289 }{ 576 }\).

A bag contains \(n\) counters.

6 of the counters are red and the other \(n - 6\) counters are blue.

Two counters are taken from the bag at random, without replacement.

The probability that both counters are red is \(\frac{1}{ 29 }\).

A bag contains 30 counters. Some of the counters are red and the rest are blue.

Two counters are taken from the bag at random, without replacement.

The probability that both counters are red is \(\frac{3}{29}\).

Work out how many red counters are in the bag.

A bag contains only red counters and green counters.

A counter is taken from the bag at random. The probability that it is red is \(\frac{1}{3}\).

The counter is put back, and then 9 more red counters are put into the bag.

A counter is now taken from the bag at random. The probability that it is red is \(\frac{1}{2}\).

Calculate how many counters were in the bag to start with.

There are only green balls and yellow balls in a bag.

The number of green balls to the number of yellow balls is in the ratio \(4 : 5\).

Leila takes at random one ball from the bag. She records the colour of the ball and then replaces it in the bag.

Leila does this \(n\) times, where \(n \geq 2\).

State an expression, in terms of \(n\), for the probability that Leila gets at least one green ball and at least one yellow ball.

The Venn diagram gives information about the number of plants in a collection.

E = all the plants, A = flowering plants, B = scented plants

One plant is taken at random from the collection.

Given that the plant is scented, the probability that it is flowering is \(\frac{ 3 }{ 4 }\).

Calculate the number of plants in the collection.

There is a total of \(y\) counters in a box.

There are \(x\) pink counters and 8 blue counters in the box.

The rest of the counters are green.

\(x : y = 1 : 3\)

Grace takes at random two counters from the box.

Find, in terms of \(x\), an expression for the probability that Grace takes two counters of the same colour.

Give your answer as a single fraction in the form \(\frac{ ax^2 + bx + c }{ dx^2 + ex }\) where \(a\), \(b\), \(c\), \(d\) and \(e\) are integers.

There are only \(u\) red counters and \(g\) green counters in a bag.

A counter is taken at random from the bag. The probability that the counter is green is \(\frac{2}{5}\).

The counter is put back in the bag. 2 more red counters and 6 more green counters are put in the bag.

A counter is taken at random from the bag. The probability that the counter is green is \(\frac{5}{9}\).

Find the number of red counters and the number of green counters that were in the bag originally.