Question

Help, please. It is a probability question.

Answer 1

P=0.1227

P=12.27%

Explanation:

Pita has 12 coins in her bag. 3 of those coins are £1 coins and 9 are £0.50.

She takes 3 coins from her bag at random. We want to calculate the probability that she takes exactly £2.50.

To take £2.50, there is only one way to combine three coins:

Two of £1 and one of £0.50

The £1 coins can be extracted from the 3 available

The £0.50 coin can be extracted from the 9 available.

The combination of both events can be calculated as:

`\displaystyle \binom{3}{2}\binom{9}{1}`

The sample space is the total combination of possible events:

`\displaystyle \binom{12}{3}`

And the probability is:

`\displaystyle P=\frac{\binom{3}{2}\binom{9}{1}}{\binom{12}{3}}`

`\displaystyle P=(3*9)/(220)`

P=0.1227

P=12.27%