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Pit has 12 coins in her bag; there are 3 £1 coins and nine 50p coins. She takes 3 coins at random from her bag. Work out the probability she takes exactly £2.50.

a. 1/22
b. 1/11
c. 1/44
d. 1/33

User Sam Skuce
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Final answer:

To determine the probability that Pit takes exactly £2.50, we calculate the probability of selecting two £1 coins and one 50p coin from the bag. Multiplying the probabilities of each selection gives us a result of 1/24.5, which does not match any of the provided options, suggesting an error in the question or choices.

Step-by-step explanation:

To find the probability that Pit takes exactly £2.50 from her bag, we need to consider the combination of coins that could sum to this amount. To make £2.50, Pit must take either two £1 coins and one 50p coin or one £1 coin and three 50p coins. The latter is not possible since she's only taking three coins in total, so the only combination she can take is two £1 coins and one 50p coin.

Step 1: Calculate the probability of taking two £1 coins and one 50p coin from the bag. There are 3 £1 coins out of 12 total, and 9 50p coins out of 12 total.

Step 2: The probability of picking the first £1 coin is 3/12. After taking one £1 coin, there are 2 £1 coins left and 11 coins in total, so the probability of picking a second £1 coin is 2/11. Lastly, there are 9 50p coins left out of the 10 remaining coins, so the probability of then picking a 50p coin is 9/10.

Step 3: Multiply these probabilities to find the total probability of the selected combination: (3/12) x (2/11) x (9/10) = 54/1320 = 1/24.5, which is not one of the provided options, indicating that there may be a mistake in the setup of the problem or in the provided options.

User Krishna Murti
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7.6k points
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