Answer:
P=0.1227
P=12.27%
Step-by-step 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:
[tex]\displaystyle \binom{3}{2}\binom{9}{1}[/tex]
The sample space is the total combination of possible events:
[tex]\displaystyle \binom{12}{3}[/tex]
And the probability is:
[tex]\displaystyle P=\frac{\binom{3}{2}\binom{9}{1}}{\binom{12}{3}}[/tex]
[tex]\displaystyle P=\frac{3*9}{220}[/tex]
P=0.1227
P=12.27%
