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19 March, 08:35

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

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  1. 19 March, 10:30
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    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.
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