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 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 8 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 blue buttons and red buttons in a tin.

The number of blue buttons to the number of red buttons is in the ratio \(3 : 5\).

Nadia takes at random one button from the tin. She records the colour of the button and then replaces it in the tin.

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

Write down an expression, in terms of \(n\), for the probability that Nadia gets at least one blue button and at least one red button.

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 \(\frac{3}{7}\).

The counter is put back in the bag. 4 more red counters and 5 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 \(\frac{7}{15}\).

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

A bag contains red, blue and green counters.

The number of red counters is \(x + 6\).

The number of blue counters is \(3x + 6\).

The number of green counters is \(3x + 6\).

A counter is taken from the bag at random. The probability that it is blue is \(\frac{9}{22}\).

A spinner can land on red, blue, green or yellow.

The table gives the probability of each colour.

A bag contains \(15\) cubes. Some of them are green and the rest are white.

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

She then takes a second cube at random from the bag.

The probability that both cubes are green is \(\frac{ 169 }{ 225 }\).

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 \(\frac{1}{4}\).

The counter is put back, and then 6 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 \(\frac{2}{5}\).

Work out how many counters were in the bag to start with.