Pita has 12 coins in her bag there are three 1 pound coins and nine 50p coins she takes 3 coins out of the bag at random, work out the probability she takes out exactly £2.50

Let's find the number of 1 pound coins and 50 pence coins that yield us 2.50 pounds.

Let x = number of 1 pound coins

y = number of 50 pence coins

Then 1x + 0.50y = 2.50

and x + y = 3

From the second equation, we get x = 3 - y.

Then substitute it into the first equation:

1 (3 - y) + 0.50y = 2.50

3 - y + 0.50y = 2.50

3 - 0.50y = 2.50

Subtract 3 from both sides:

-0.50y = - 0.50

Divide both sides by - 0.50:

y = 1

Then x = 3 - 1 = 2

So to make 2.50 pounds, she need to take two 1 pound coins and one 50 pence coin.

Next, we have to find the probability that she takes exactly two 1 pound coins and one 50 pence coin. That should be

P = (3C2) • (9C1) / (12C3) = 0.1227

So the answer is 0.1227.