Question

pita has 12 coins in her bag there are three £1 coins and nine 50p coins she takes 3 coins from the bag at random work out theprobability that she takes exactly £2.50

Answer 1

The probability of taking exactly £2.50 from the bag is 9/55.

Step-by-step explanation:

To calculate the probability of taking exactly £2.50 from the bag, we need to consider the number of ways we can choose the coins that add up to £2.50, divided by the total number of ways we can choose any 3 coins from the bag.

First, let's calculate the total number of ways we can choose any 3 coins from 12. This can be done using the combination formula: C(12, 3) = 12! / (3! * (12-3)!) = 220.

Next, let's consider the different combinations of coins that can add up to £2.50. We can have (1 £1 coin, 1 50p coin) or (1 50p coin, 2 £1 coins).

For the first combination, there are 3 ways to choose a £1 coin and 9 ways to choose a 50p coin. Therefore, there are 3 * 9 = 27 ways to choose the first combination of coins.

For the second combination, there are 3 ways to choose a 50p coin and 3 ways to choose a £1 coin (since we already used one in the previous combination). Therefore, there are 3 * 3 = 9 ways to choose the second combination of coins.

Adding up the ways for each combination, we have a total of 27 + 9 = 36 ways to choose coins that add up to £2.50.

Finally, we can calculate the probability by dividing the number of favorable outcomes (ways to choose coins that add up to £2.50) by the total number of outcomes (ways to choose any 3 coins from the bag): 36 / 220 = 9 / 55.